Validation of Marine Geoid Models by Profile-wise GNSS Measurements on Ice Surface

Ship-board global navigation satellite system (GNSS) measurements are widely used to determine sea surface heights, marine geoid validation, and/or satellite altimetry calibration. However, the use of a vessel could be complicated near coastal areas due to shallow water. Therefore, in the area of sea ice formation, GNSS measurements on the ice surface could be a viable alternative to vessel-borne surveys. Importantly, the ice-covered water is not affected by short-term winds, which otherwise could have systematic influence on the instantaneous sea surface topography. This study tackles methodology and validation of marine geoid models by profile-wise GNSS measurements on ice in an archipelago of the Baltic Sea. The GNSS measurements were carried out on the three ice roads with total length 48 kilometers. The along-route standard deviation between the gravimetric geoid model and profile-wise GNSS heights remained within ±2.1 centimeters.     

Improving the Coastal Mean Dynamic Topography by Geodetic Combination of Tide Gauge and Satellite Altimetry

Abstract

The ocean mean dynamic topography (MDT) is the surface representation of the ocean circulation. The MDT may be determined by the ocean approach, which involves temporal averaging of numerical ocean circulation model information, or by the geodetic approach, wherein the MDT is derived using the ellipsoidal height of the mean sea surface (MSS), or mean sea level (MSL) minus the geoid as the geoid. The ellipsoidal height of the MSS might be estimated either by satellite or coastal tide gauges by connecting the tide gauge datum to the Earth-centred reference frame. In this article we present a novel approach to improve the coastal MDT, where the solution is based on both satellite altimetry and tide gauge data using new set of 302 tide gauges with ellipsoidal heights through the SONEL network. The approach was evaluated for the Northeast Atlantic coast where a dense network of GNSS-surveyed tide gauges is available. The typical misfit between tide gauge and satellite or oceanographic MDT was found to be around 9?cm. This misfit was found to be mainly due to small scale geoid errors. Similarly, we found, that a single tide gauge places only weak constraints on the coastal dynamic topography.     

First Calibration Results for the SARAL/AltiKa Altimetric Mission Using the Gavdos Permanent Facilities

This work presents the first calibration results for the SARAL/AltiKa altimetric mission using the Gavdos permanent calibration facilities. The results cover one year of altimetric observations from April 2013 to March 2014 and include 11 calibration values for the altimeter bias. The reference ascending orbit No. 571 of SARAL/AltiKa has been used for this altimeter assessment. This satellite pass is coming from south and nears Gavdos, where it finally passes through its west coastal tip, only 6 km off the main calibration location. The selected calibration regions in the south sea of Gavdos range from about 8 km to 20 km south off the point of closest approach. Several reference surfaces have been chosen for this altimeter evaluation based on gravimetric, but detailed regional geoid, as well as combination of it with other altimetric models.

Based on these observations and the gravimetric geoid model, the altimeter bias for the SARAL/AltiKa is determined as mean value of ?46mm ±10mm, and a median of ?42 mm ±10 mm, using GDR-T data at 40 Hz rate. A preliminary cross-over analysis of the sea surface heights at a location south of Gavdos showed that SARAL/AltiKa measure less than Jason-2 by 4.6 cm. These bias values are consistent with those provided by Corsica, Harvest, and Karavatti Cal/Val sites. The wet troposphere and the ionosphere delay values of satellite altimetric measurements are also compared against in-situ observations (?5 mm difference in wet troposphere and almost the same for the ionosphere) determined by a local array of permanent GNSS receivers, and meteorological sensors.     

Applications of satellite altimetry to oceanography and geophysics

Satellite-borne altimeters have had a profound impact on geodesy, geophysics, and physical oceanography. To first order approximation, profiles of sea surface height are equivalent to the geoid and are highly correlated with seafloor topography for wavelengths less than 1000 km. Using all available Geos-3 and Seasat altimeter data, mean sea surfaces and geoid gradient maps have been computed for the Bering Sea and the South Pacific. When enhanced using hill-shading techniques, these images reveal in graphic detail the surface expression of seamounts, ridges, trenches, and fracture zones. Such maps are invaluable in oceanic regions where bathymetric data are sparse. Superimposed on the static geoid topography is dynamic topography due to ocean circulation. Temporal variability of dynamic height due to oceanic eddies can be determined from time series of repeated altimeter profiles. Maps of sea height variability and eddy kinetic energy derived from Geos-3 and Seasat altimetry in some cases represent improvements over those derived from standard oceanographic observations. Measurement of absolute dynamic height imposes stringent requirements on geoid and orbit accuracies, although existing models and data have been used to derive surprisingly realistic global circulation solutions. Further improvement will only be made when advances are made in geoid modeling and precision orbit determination. In contrast, it appears that use of altimeter data to correct satellite orbits will enable observation of basin-scale sea level variations of the type associated with climatic phenomena.     

Sea Surface Heights Retrieval from Ship-Based Measurements Assisted by GNSS Signal Reflections

Measurements of the sea surface height (SSH) can be carried out with GNSS aboard ships, but data about the static draft and the hydrodynamic squat effect are necessary. This information is often not available or has an insufficient accuracy. In this study, an alternative method based on the GNSS signal-to-noise ratio observations is presented. Using this method, the distance between the water surface and a GNSS antenna can be estimated directly, if corrections of the heave and the ship’s attitude are considered properly. Suitable segments of a 3-month dataset, gathered aboard a ferry ship operating in the German Bight, were analysed. A global optimization approach based on interval analysis was used and all available observations from a segment were analysed in a common adjustment calculation. The resulting SSH was validated with data from a tide gauge station at Heligoland. The mean difference is 4?mm and a standard deviation of the differences of 5.3?cm was found. The SSH for the same GNSS dataset was also derived from a well-established processing based on the comprehensive consideration of ship dynamics. The mean difference with respect to the tide gauge was 2?mm with a slightly smaller standard deviation of 4.0?cm.     

The Role of Multi-Mission ERS Altimetry in the Determination of the Marine Geoid in the Azores

This study concerns the determination of a regional geoid model in the North Atlantic area surrounding the Azores islands by combining multi-mission altimetry from the ERS (European Remote Sensing) satellites and surface gravity data. A high resolution mean sea surface, named AZOMSS99, has been derived using altimeter data from ERS-1 and ERS-2 35-day cycles, spanning a period of about four years, and from ERS-1 geodetic mission. Special attention has been paid to data processing of points around the islands due to land contamination on some of the geophysical corrections. A gravimetric geoid has been computed from all available surface gravity, including land and sea observations acquired during an observation campaign that took place in the Azores in October 1997 in the scope of a European and a Portuguese project. Free air gravity anomalies were derived by altimetric inversion of the mean sea surface heights. These were used to fill the large gaps in the surface gravity and combined solutions were computed using both types of data. The gravimetric and combined solutions have been compared with the mean sea surface and GPS (Global Positioning System)-levelling derived geoid undulations in five islands. It is shown that the inclusion of altimeter data improves geoid accuracy by about one order of magnitude. Combined geoid solutions have been obtained with an accuracy of better than one decimetre.     

基于GNSS浮标和验潮资料的HY-2A卫星高度计绝对定标

为探测我国HY-2A卫星高度计海面高测量绝对偏差及其在轨运行状态,本文利用GNSS浮标星下点同步测量和验潮资料海面高传递方法在山东千里岩和珠海担杆岛海域开展定标研究。为验证GNSS浮标定标方法的准确性,还对国外卫星Jason-2和Saral进行了定标实验。实验表明GNSS浮标绝对海面高测量精度达2 cm,对Jason-2和Saral高度计多个周期定标得到的海面高偏差均值分别为5.7 cm和-2.3 cm,与国际专门定标场的结果符合较好。2014年9月和2015年5月HY-2A卫星高度计浮标定标结果分别是-65 cm和-91 cm,因两次结果差异显著,故又利用千里岩验潮站资料对HY-2A卫星高度计第56至73周期进行了定标分析,结果证明HY-2A卫星海面高存在约-51 cm/a的漂移,置信度为95%的回归分析表明浮标和验潮定标结果符合。本文研究结果表明在我国尚无专门定标场的情况下,可利用GNSS浮标对我国高度计实施灵活、精准的在轨绝对定标,在有高度计轨迹经过验潮站的情况下可使用验潮资料结合精密大地水准面模型进行绝对定标。     

The Role of Multi-Mission ERS Altimetry in the Determination of the Marine Geoid in the Azores

This study concerns the determination of a regional geoid model in the North Atlantic area surrounding the Azores islands by combining multi-mission altimetry from the ERS (European Remote Sensing) satellites and surface gravity data. A high resolution mean sea surface, named AZOMSS99, has been derived using altimeter data from ERS-1 and ERS-2 35-day cycles, spanning a period of about four years, and from ERS-1 geodetic mission. Special attention has been paid to data processing of points around the islands due to land contamination on some of the geophysical corrections. A gravimetric geoid has been computed from all available surface gravity, including land and sea observations acquired during an observation campaign that took place in the Azores in October 1997 in the scope of a European and a Portuguese project. Free air gravity anomalies were derived by altimetric inversion of the mean sea surface heights. These were used to fill the large gaps in the surface gravity and combined solutions were computed using both types of data. The gravimetric and combined solutions have been compared with the mean sea surface and GPS (Global Positioning System)-levelling derived geoid undulations in five islands. It is shown that the inclusion of altimeter data improves geoid accuracy by about one order of magnitude. Combined geoid solutions have been obtained with an accuracy of better than one decimetre.     

High Precision Geoid Models HKGEOID-2000 for Hong Kong and SZGEOID-2000 for Shenzhen, China

High precision geoid models HKGEOID-2000 for Hong Kong and SZGEOID-2000 for Shenzhen, China, have been developed with a hybrid approach of so-called sequential processing, using high precision GPS/leveling data, land and sea gravity anomalies, and digital terrain models. These two local geoid models have the same 1-km resolution. The estimated accuracy (external accuracy) is better than 1.7 cm for HKGEOID-2000 and 1.4 cm for SZGEOID-2000. Some common areas are covered by HKGEOID-2000 and SZGEOID-2000. So these two geoid models, along with high quality GPS/leveling data collected on the overlapping areas, can be used to detect the systematic bias between HKGEOID-2000 and SZGEOID-2000, as well as the difference between Hong Kong Principal Datum and 1956 yellow sea height datum of China, yielding RMS errors of 1.011 m and 1,003 m, respectively. Moreover, HKGEOID-2000, along with GPS ellipsoidal heights, is employed to determine the errors of the “orthometric heights” from purely trigonometric heighting, yielding an RMS error of 0.102 m. The combination of SZGEOID-2000 and GPS ellipsoidal heights has been used to replace the traditional spirit leveling and mapping, called GPS mapping.     

High Precision Geoid Models HKGEOID-2000 for Hong Kong and SZGEOID-2000 for Shenzhen,China

High precision geoid models HKGEOID-2000 for Hong Kong and SZGEOID-2000 for Shenzhen, China, have been developed with a hybrid approach of so-called sequential processing, using high precision GPS/leveling data, land and sea gravity anomalies, and digital terrain models. These two local geoid models have the same 1-km resolution. The estimated accuracy (external accuracy) is better than 1.7 cm for HKGEOID-2000 and 1.4 cm for SZGEOID-2000. Some common areas are covered by HKGEOID-2000 and SZGEOID-2000. So these two geoid models, along with high quality GPS/leveling data collected on the overlapping areas, can be used to detect the systematic bias between HKGEOID-2000 and SZGEOID-2000, as well as the difference between Hong Kong Principal Datum and 1956 yellow sea height datum of China, yielding RMS errors of 1.011 m and 1,003 m, respectively. Moreover, HKGEOID-2000, along with GPS ellipsoidal heights, is employed to determine the errors of the “orthometric heights” from purely trigonometric heighting, yielding an RMS error of 0.102 m. The combination of SZGEOID-2000 and GPS ellipsoidal heights has been used to replace the traditional spirit leveling and mapping, called GPS mapping.     

Precise Geoid Determination over Hong Kong from Heterogeneous Data Sets using a Hybrid Method

ABSTRACT

This study attempts to develop a methodology to construct a high-precision geoid model (HKGEOID-2016) over Hong Kong. To achieve this objective, a hybrid method is employed in this article. The proposed method involves three steps: the combination of multisource data; the construction of gravimetric geoid model using the remove-restore technique and Molodensky's theory; and the optimal combination of heterogeneous height data, improved by the evaluation of stochastic models through the variance component estimation method and assessment of the parametric model. The accuracy of the constructed geoid is evaluated with independent GNSS/leveling data. Numerical results indicate that external precision of 1.5 cm level is achievable. Furthermore, compared with the former geoid model HKGEOID-2000, the proposed procedure in this study improves the accuracy of the geoid significantly.     

Combined satellite altimetry and shipborne gravimetry data processing

The recovery of quantities related to the gravity field (i.e., geoid heights and gravity anomalies) is carried out in a test area of the central Mediterranean Sea using 5' × 5' marine gravity data and satellite altimeter data from the Geodetic Mission (GM) of ERS‐J. The optimal combination of the two heterogeneous data sources is performed using (1) the space‐domain least‐squares collocation (LSC) method, and (2) the frequency‐domain input‐output system theory (IOST). The results derived by these methods agree at the level of 2 cm in terms of standard deviation in the case of the geoid height prediction. The gravity anomaly prediction results by the same methods vary between 2.18 and 2.54 mGal in terms of standard deviation. In all cases, the spectral techniques have a much higher computational efficiency than the collocation procedure. In order to investigate the importance of satellite altimetry for gravity field modeling, a pure gravimetric geoid solution, carried out in a previous study for our lest area by the fast collocation approach (FCOL), is used in comparison with the combined geoid models. The combined solutions give more accurate results, at the level of about 15 cm in terms of standard deviation, than the gravimetric geoid solution, when the geoid heights derived by each method are compared with TOPEX altimeter sea surface heights (SSHs). Moreover, nonisotropic power spectral density functions (PSDs) can be easily used by IOST, while LSC requires isotropic covariance functions. The results show that higher prediction accuracies are always obtained when using a priori nonisotropic information instead of isotropic information.     

Steric height trends at Ocean Station Papa in the Northeast Pacific Ocean

Abstract

We estimate secular changes in steric sea level in the northeast Pacific Ocean using the 27‐year time series of monthly hydrographic observations for Station PAPA (50°N, 145°W). Linear trends based on the entire data record suggest that steric heights relative to 1000 db are increasing at a rate of 0.93 mm/yr and that 67% of this increase is due to thermosteric changes at depths below 100 m; the smaller halosteric contribution to the steric trend appears to be confined to the upper 100 m. A trend of 0(1 mm/yr) is consistent with estimates of sea level rise based on coastal tide gauge records. However, a critical examination of the results indicates that sea level changes of such small magnitude would be masked by the large (1–10 cm) interannual variability of open ocean steric height. This is verified by recalculation of trends using abridged versions of the data set. We conclude that our trend estimates are still open to question and that the present 27‐year time series is too short to permit accurate resolution of possible climate‐induced changes in global sea level.     

Global ocean circulation patterns based on seasat altimeter data and the GEML2 gravity field

The Seasat altimeter data has been completely adjusted by a crossing arc technique to reduce the crossover discrepancies to approximately ±30 cm in five regional adjustments. This data was then used to create sea surface heights at 1° intersections in the ocean areas with respect to the GRS80 ellipsoid. These heights excluded the direct tidal effects but included the induced permanent deformation. A geoid corresponding to these sea surface heights was computed, based on the potential coefficients of the GEML2 gravity field up to degree 6, augmented by Rapp's coefficients up to degree 180. The differences between sea surface heights and the geoid were computed to give approximate estimates of sea surface topography. These estimates are dominated by errors in both sea surface heights and geoid undulations. To optimally determine sea surface topography a spherical harmonic analysis of raw estimates was carried out and the series was further truncated at degree 6, giving estimates with minimum wavelengths on the order of 6000 km. The direction of current flow can be computed on a global basis using the spherical harmonic expansion of the sea surface topography. Ths has been done, not only for Seasat/GEML2 estimates, but also using the recent dynamic topography estimates of Levitus. The results of the two solutions are very similar and agree well with the major circulation features of the oceans.     

Absolute Calibration of the Jason-1 Altimeter Using UK Tide Gauges

This article describes an “absolute” calibration of Jason-1 (J-1) altimeter sea surface height bias using a method developed for TOPEX/Poseidon (T/P) bias determination reported previously. The method makes use of U.K. tide gauges equipped with Global Positioning System (GPS) receivers to measure sea surface heights at the same time, and in the same geocentric reference frame, as Jason-1 altimetric heights recorded in the nearby ocean. The main time-dependent components of the observed altimeter-minus-gauge height-difference time series are due to the slightly different ocean tides at the gauge and in the ocean. The main harmonic coefficients of the tide differences are calculated from analysis of the copious TOPEX data set and then applied to the determination of T, P, and J-1 bias in turn. Datum connections between the tide gauge and altimetric sea surface heights are made by means of precise, local geoid differences from the EGG97 model. By these means, we have estimated Jason-1 altimeter bias determined from Geophysical Data Record (GDR) data for cycles 1-61 to be 12.9 cm, with an accuracy estimated to be approximately 3 cm on the basis of our earlier work. This J-1 bias value is in close agreement with those determined by other groups, which provides a further confirmation of the validity of our method and of its potential for application in other parts of the world where suitable tide gauge, GPS, and geoid information exist.     

Absolute Calibration of the Jason-1 Altimeter Using UK Tide Gauges

This article describes an “absolute” calibration of Jason-1 (J-1) altimeter sea surface height bias using a method developed for TOPEX/Poseidon (T/P) bias determination reported previously. The method makes use of U.K. tide gauges equipped with Global Positioning System (GPS) receivers to measure sea surface heights at the same time, and in the same geocentric reference frame, as Jason-1 altimetric heights recorded in the nearby ocean. The main time-dependent components of the observed altimeter-minus-gauge height-difference time series are due to the slightly different ocean tides at the gauge and in the ocean. The main harmonic coefficients of the tide differences are calculated from analysis of the copious TOPEX data set and then applied to the determination of T, P, and J-1 bias in turn. Datum connections between the tide gauge and altimetric sea surface heights are made by means of precise, local geoid differences from the EGG97 model. By these means, we have estimated Jason-1 altimeter bias determined from Geophysical Data Record (GDR) data for cycles 1–61 to be 12.9 cm, with an accuracy estimated to be approximately 3 cm on the basis of our earlier work. This J-1 bias value is in close agreement with those determined by other groups, which provides a further confirmation of the validity of our method and of its potential for application in other parts of the world where suitable tide gauge, GPS, and geoid information exist.     

The Role of GNSS Vertical Velocities to Correct Estimates of Sea Level Rise from Tide Gauge Measurements in Greece

In this study, we show how the Global Navigation Satellite System (GNSS)-derived vertical velocities contribute to the correction of tide gauge (TG) measurements used for the sea level rise estimation in Greece. Twelve sites with records of local sea level heights are processed in order to estimate their trend. Certain error sources related to TGs, e.g. equipment changes, data noise, may lead to biased or erroneous estimations of the sea level height. Therefore, it would be preferred to follow a robust estimation technique in order to detect and reduce outlier effects. The geocentric sea level rise is estimated by taking into account the land vertical motion of co-located GNSS permanent stations at the Hellenic area. TGs measure the height of the water relative to a monitored geodetic benchmark on land. On the other hand, using GNSS-based methods the vertical land motion can be derived. By means of extended models fitted to the GNSS time-series position, obtained from seven years of continuous data analysis, periodic signals are well described. The synergy of the two co-located techniques results in the correction of TG relative sea level heights taking into account the GNSS vertical velocities and consequently obtaining the conversion to absolute (geocentric) sea level trend.     

Comparison of geosat and gravimetric geoid profiles in the North Sea

Sea surface height profiles derived from 2‐year, repeat track, Geosat altimeter data have been compared with a regional gravimetric geoid in the western North Sea, computed using a geopotential model and terrestrial gravity data. The comparison encompasses 18 Geosat profiles covering a 750 × 850 km area of the North Sea. After a second‐order polynomial was used to model the long‐wavelength differences which cannot be clearly separated over an area of this size, results show agreement to better than ±3 cm for wavelengths between approximately 20 and 750 km. In regions where terrestrial gravity data were not available to improve the geoid, similar comparisons with the OSU91A geopotential model alone show differences of up to ±6 cm. This illustrates the importance of incorporating local gravity data in regional geoid computations, and partly validates the regional gravimetric geoid solution and Geosat sea surface profiles in the western North Sea. It is concluded that, in marine areas where the sea surface topography is known to be small in magnitude, Geosat sea surface profiles can act as an independent control on gravimetric geoids in the medium‐wavelength range.     

Heterogeneous Gravity Data Fusion and Gravimetric Quasigeoid Computation in the Coastal Area of China

ABSTRACT

Different types of gravity observations are available over coastal areas. The main challenge for coastal geoid determination is the proper fusion of heterogeneous gravity data including land, shipborne, airborne, and altimetry-derived gravity data. This paper describes the gravity data fusion and the computation of the gravimetric quasigeoid in the coastal area of mainland China. An iterative procedure of the weighted least-squares prediction based on rectangular harmonic functions is used for merging the land, altimetric, shipborne, and airborne gravity data. Applying the analytical continuation method in Molodensky's theoretic frame, the merged gravity data are then used to determine the gravimetric quasigeoid model by using the generalized Stokes' integral in a remove-compute-restore fashion. The gravimetric quasigeoid model is compared with the height anomalies determined at 662 GPS leveling points over the coastal region of mainland China, where both the geodetic height and the normal height are known. The standard deviations of the differences in the coastal provinces range from 1.8 to 4.4 cm. For the entire computation area, the mean and standard deviation of the differences are 27.9 and 3.9 cm, respectively.     

Improvement in the Determination of the Marine Geoid by Estimating the Bathymetry from Altimetry and Depth Soundings

Abstract

The contribution of bathymetry to the estimation of gravity field related quantities is investigated in an extended test area in the Mediterranean Sea. The region is located southwest of the island of Crete, Greece, bounded between 33^? ≤ ? ≤ 35^? and 15^? ≤ λ ≤ 25^?. Gravity anomalies from the KMS99 gravity field and shipborne depth soundings are used with a priori statistical characteristics of depths in a least-squares collocation procedure to estimate a new bathymetry model. Two different global bathymetry models, namely JGP95E and Sandwell and Smith V8, are used to derive the depth a priori statistical information, while the estimated model is compared against both the global ones and the shipborne depth soundings to assess whether there is an improvement. Various marine geoid models are estimated using ERS1 and GEOSAT Geodetic Mission altimetry and shipborne gravity data. In that process, the effect of the bathymetry is computed using both the estimated and the original depths through a residual terrain modeling reduction. The TOPEX/Poseidon Sea Surface Heights, known for their high accuracy and precision, and the GEOMED solution for the geoid in the Mediterranean are used as control for the validation of the new geoid models and to assess the improvement that the estimated depths offer to geoid modeling. The results show that the newly estimated bathymetry agrees better (by about 30 to 300 m) with the shipborne depth soundings and provides smoother residual geoid heights and gravity anomalies (by about 8–20%) than those from global models. Finally, the achieved accuracy in geoid modeling ranges between 6 and 10 cm (1σ).