Estimating the sea surface dynamic topography from Geosat altimetry data

Optimal interpolation method is applied to Geosat altimetry data both to remove orbit error and to separate temporal mean sea surface dynamic topography (SSDT) from temporal fluctuations around the mean. Loss of long-wavelength oceanic signals at orbit error reduction procedure is smaller in this method than that in conventional collinear methods, but the areal average height over the study domain is still removed as the orbit error. The fluctuation SSDT is quantitatively evaluated by sea level data from tide gauge stations at Japanese islands. The correlation coefficient of the two sea-level variations is 0.83 when the loss of the areal average is compensated by the seasonal variation of the areal average height determined from the climatological monthly-mean SSDT. In addition, the improvement of the geoid model by combined use of Seasat altimetry data and hydrographic data is validated through the estimated temporal mean SSDT. In a local area where hydrographic data contemporary with the Seasat mission exist, the geoid model has been significantly improved so that the absolute SSDT can be determined from combination of the altimetry data and geoid model; the absolute SSDT describes the onset event of a quasi-stationary large meander of the Kuroshio south of Japan very well. Outside this local area, however, errors of several tens of centimeters still remain in the improved geoid model.     

Consistency of Geoid Models,Radar Altimetry,and Hydrodynamic Modelling in the North Sea

Radar altimetry, when corrected for tides, atmospheric forcing of the sea surface, and the effects of density variations and mean and time-variable currents, provides an along-track realization of the marine geoid. In this study we investigate whether and how such an ‘altimetric-hydrodynamic’ geoid over the North Sea can serve for validating satellite-gravimetric geoids. Our results indicate that, using ERS-2 and ENVISAT along-track altimetry and water levels from the high-resolution operational circulation model BSHcmod, we do find distinct differences in RMS fits for various state-of-the art satellite-only models (beyond degree 145 for GRACE-only, and beyond degree 185 for GOCE models) and for combined geoid models, very similar as seen in GPS-levelling validations over land areas. We find that, at spectral resolution of up to about 200, an RMS fit as low as about 7 cm can be obtained for the most recent GOCE-derived models such as GOCO05S. This is slightly above what we expect from budgeting individual errors. Key to the validation is a proper treatment of the spectral mismatch between satellite-gravimetric and altimetric-hydrodynamic geoids. Comparison of data fits and error budget suggests that geoid truncation errors residual to EGM2008 (i.e. EGM2008 commission and omission error) may amount up to few cm.     

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.     

Computerized detection of seamounts from Seasat type geodetic data

Abstract

Geoid heights and vertical deflections derived from satellite radar altimetry contain characteristic signals that may be reproduced and explained by simple models for seamount gravitation acting on the sea surface. Computer algorithms capable of automatic operation and able to detect, approximately locate, and estimate parameters constraining the shape of actual sea‐mounts were written and tested. The computer program which utilized a digital high‐pass filter combined with a roughness sensor was effective in separating the seamount produced geoid undulation/vertical deflection pattern from the remaining data track features, simultaneously detecting and locating along the track such signals. Tests of the algorithm on several SEASAT passes over known bathymetry produced mixed results. Meaningful shape constraints were obtained by matching the geoid anomaly calculated from the seamount model to the actual mean sea level pattern for some seamounts. Results for other seamounts were poor and possible reasons for the failure are discussed. It is concluded that a computerized seamount detection program for radar altimetry data is feasible, but it will have to be more complex than the present one for fully successful operation.     

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.     

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.     

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.     

卫星测高技术在监测海啸现象中的研究及应用

利用卫星测高技术,通过共线平差和沿轨、垂直轨迹测高大地水准面梯度的计算,得到了海啸发生2个小时后的海面波高和海面梯度异常现象,为利用卫星测高技术监测海啸、模拟海啸现象提供了依据。     

Determining the Gravitational Gradient Tensor Using Satellite-Altimetry Observations over the Persian Gulf

With the advent of satellite altimetry in 1973, new scientific applications became available in oceanography, climatology, and marine geosciences. Moreover, satellite altimetry provides a significant source of information facilitated in the geoid determination with a high accuracy and spatial resolution. The information from this approach is a sufficient alternate for marine gravity data in the high-frequency modeling of the marine gravity field quantities. The gravity gradient tensor, consisting of the second-order partial derivatives of the gravity potential, provides more localized information than gravity measurements. Marine gravity observations always carry a high noise level due to environmental effects. Moreover, it is not possible to model the high frequencies of the Earth's gravity field in a global scale using these observations. In this article, we introduce a novel approach for a determination of the gravity gradient tensor at sea level using satellite altimetry. Two numerical techniques are applied and compared for this purpose. In particular, we facilitate the radial basis functions (RBFs) and the harmonic splines. As a case study, the gravitational gradient tensor is determined and results presented in the Persian Gulf. Validation of results reveals that the solution of the harmonic spline approach has a better agreement with a theoretical zero-value of the trace of the Marussi gravitational gradient tensor. However, the data-adaptive technique in the RBF approach allows more efficient selection of the parameters and 3-D configuration of RBFs compared to a fixed parameterization by the harmonic splines.     

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).     

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

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^ˆ ≤ ϕ ≤ 35^ˆ and 15^ˆ ≤ λ ≤ 25^ˆ. 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).     

多源数据推求的西太平洋区域海面动力地形比较分析

简述利用空间大地测量观测数据和海洋水文数据推求海面动力地形的方法。基于EGM96重力场模型和卫星重力恢复的重力场模型GL04C,联合卫星测高平均海面高模型分别推算西太平洋海域的平均海面动力地形,并与根据海洋水文数据推算之结果进行比较分析。结果表明:卫星重力场模型GL04C更好地表现了海面地形的细节特征。卫星重力和卫星测高的联合应用将成为确定海面动力地形的有效途径之一。     

Global point‐mass adjustment of the oceanic geoid based on satellite altimetry

Altimeter residuals from a global spherical‐harmonic adjustment of satellite altimetry can be used as observations in a subsequent, or second‐phase, adjustment of a short‐wavelength oceanic geoid in terms of point‐mass magnitudes as parameters. An important part of the development presented is the formulation of the second‐phase adjustment via a banded or a banded‐bordered system of normal equations. This task encompasses three separate features: (1) elimination of the point masses from an observation equation if they are sufficiently far from the pertinent observation point, (2) special arrangement of the point‐mass parameters in the adjustment scheme, and (3) resolution of the resulting system through an adaptation of the well‐known Choleski algorithm. If only the point‐mass magnitudes are subject to adjustment, one is concerned with a banded system of normal equations. If selected tidal parameters are also implicated, this system becomes banded‐bordered. In fact, the former is a special case of the latter in every respect. By virtue of this approach (with or without tidal parameters), geoid undulations over large ocean basins can be adjusted in a few overlapping strips of point masses, leading to a detailed resolution of the entire oceanic geoid.     

Oceanic gravity by analytical inversion of Hotine's formula

An analytical inversion of the Hotine formula is developed using fast Fourier transform techniques. Detailed mathematical derivations are used to explain the concepts behind the inverse transformation. Three modifications of the analytical inversion of the Hotine formula are compared and tested using both synthetic data from the OSU91A geopotential model and real GEOSAT altimetry data from the Exact Repeat Mission. The stability of this inverse Hotine approach is investigated using simulated data, and numerical tests are done to quantify the stability of this approach. The approach seems to be numerically stable without employing any stabilization technique. Estimated gravity information from GEOSTAT altimetry data is compared to marine gravity data from shipboard measurements in the Orphan Knoll area. The standard deviations and mean values of the differences between satellite and marine gravity disturbances are 8.2 and 2.9 mGal for the planar approximation, 9.2 and 3.7 mGal for the spherical approximation, and 9.5 and 1.9 mGal for the Molodenskii‐like approximation, respectively, indicating that latitude‐dependent errors affect the latter two approximations. Such errors could be eliminated by performing the calculations by the rigorous one‐dimensional fast Fourier transform (FFT) technique, and any data noise could be filtered out by utilizing covariance knowledge about the input geoid undulations and their errors. Simulation studies also showed that the accuracy of the techniques (for all approximations) can reach a root‐mean‐square (RMS) level of only a few mGal when proper treatment of FFT edge effects is employed and a rather wide area of results is disregarded around the edges.     

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.     

Geodetic measurements in the ocean

This paper covers the topic of marine geodesy, its goals, and applications. Specifically discussed are position determination and establishment of geodetic control on the ocean bottom, ocean surface, and subsurface, and the determination of the geoid, a vertical reference surface. The various techniques used in position determination (including satellite, airborne, radio, inertial and acoustic techniques) are assessed in terms of accuracy, coverage, and contribution to the solution of specific problems associated with position and control. The results of several marine geodetic control experiments are presented. Classical techniques for the determination of the geoid are discussed and assessed, as are new techniques such as satellite altimetry. The outlook for marine geodetic measurements in the ocean is outlined in terms of what is being planned or considered for the next decade, and several recommendations are made.     

Comparison of Satellite Altimetric Gravity and Global Geopotential Models with Shipborne Gravity in the Red Sea

The determination of high-resolution geoid for marine regions requires the integration of gravity data provided by different sources, e.g. global geopotential models, satellite altimetry, and shipborne gravimetric observations. Shipborne gravity data, acquired over a long time, comprises the short-wavelengths gravitation signal. This paper aims to produce a consistent gravity field over the Red Sea region to be used for geoid modelling. Both, the leave-one-out cross-validation and Kriging prediction techniques were chosen to ensure that the observed shipborne gravity data are consistent as well as free of gross-errors. A confidence level equivalent to 95.4% was decided to filter the observed shipborne data, while the cross-validation algorithm was repeatedly applied until the standard deviation of the residuals between the observed and estimated values are less than 1.5 mGal, which led to the elimination of about 17.7% of the shipborne gravity dataset. A comparison between the shipborne gravity data with DTU13 and SSv23.1 satellite altimetry-derived gravity models is done and reported. The corresponding results revealed that altimetry models almost have identical data content when compared one another, where the DTU13 gave better results with a mean and standard deviation of ?2.40 and 8.71 mGal, respectively. A statistical comparison has been made between different global geopotential models (GGMs) and shipborne gravity data. The Spectral Enhancement Method was applied to overcome the existing spectral gap between the GGMs and shipborne gravity data. EGM2008 manifested the best results with differences characterised with a mean of 1.35 mGal and a standard deviation of 11.11 mGal. Finally, the least-squares collocation (LSC) was implemented to combine the shipborne gravity data with DTU13 in order to create a unique and consistent gravity field over the Red Sea with no data voids. The combined data were independently tested using a total number of 95 randomly chosen shipborne gravity stations. The comparison between the extracted shipborne gravity data and DTU13 altimetry anomalies before and after applying the LSC revealed that a significant improvement is procurable from the combined dataset, in which the mean and standard deviation of the differences dropped from ?3.60 and 9.31 mGal to ?0.39 and 2.04 mGal, respectively.     

Geoid height anomalies over the Cape Verde Rise

Geoid height anomalies, as determined by satellite altimetry, suggest that the Cape Verde Rise is in local isostatic equilibrium, supported by a low-density root of altered lithosphere. A depth anomaly map shows the Cape Verde Rise to be approximately 1600 km wide and 2km high. Removal of a quadratic surface from the observed geoid heights leaves a residual positive anomaly with the same shape as the rise and an amplitude of about 8 m. The ratio of residual geoid height anomaly to depth anomaly is consistent with an isostatic root only 40 km deep on average.     

Depth to basement and geoid expression of the Kane Fracture Zone: A comparison

Geoid data from Geosat and subsatellite basement depth profiles of the Kane Fracture Zone in the central North Atlantic were used to examine the correlation between the short-wavelength geoid (=25–100 km) and the uncompensated basement topography. The processing technique we apply allows the stacking of geoid profiles, although each repeat cycle has an unknown long-wavelength bias. We first formed the derivative of individual profiles, stacked up to 22 repeat cycles, and then integrated the average-slope profile to reconstruct the geoid height. The stacked, filtered geoid profiles have a noise level of about 7 mm in geoid height. The subsatellite basement topography was obtained from a recent compilation of structure contours on basement along the entire length of the Kane Fracture Zone. The ratio of geoid height to topography over the Kane Fracture Zone valley decreases from about 20–25 cm km^-1 over young ocean crust to 5–0 cm km^-1 over ocean crust older than 140 Ma. Both geoid and basement depth of profiles were projected perpendicular to the Kane Fracture Zone, resampled at equal intervals and then cross correlated. The cross correlation shows that the short-wavelength geoid height is well correlated with the basement topography. For 33 of the 37 examined pro-files, the horizontal mismatches are 10 km or less with an average mismatch of about 5 km. This correlation is quite good considering that the average width of the Kane Fracture Zone valley at median depth is 10–15 km. The remaining four profiles either cross the transverse ridge just east of the active Kane transform zone or overlie old crust of the M-anomaly sequence. The mismatch over the transverse ridge probably is related to a crustal density anomaly. The relatively poor correlation of geoid and basement depth in profiles of ocean crust older than 130–140 Ma reflects poor basement-depth control along subsatellite tracks.     

多类资料计算南海重力垂直梯度的方法比较

重力垂直梯度在解决和解释地球表层地质和地球物理问题中的作用日益明显,因而获得其模型和分布是非常必要的。利用测高卫星可以得到空间大范围高精度、高分辨率的垂线偏差、重力异常以及大地水准面数据,利用测高重力资料和地球重力场模型,采用不同方法分别计算了南海海域重力垂直梯度,并对它们进行了比较。