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Tzong-jer Tsai - One of the best experts on this subject based on the ideXlab platform.
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the fractal properties of Sea Surface Topography derived from topex poseidon 1992 1996
Computers & Geosciences, 1999Co-Authors: Tian-yuan Shih, Jin-tsong Hwang, Tzong-jer TsaiAbstract:Fractal dimension with various algorithms has increasing applications in characterizing both linear and areal features. In this study, the variabilities of Sea Surface Topography derived from TOPEX/POSEIDON are studied. The variogram method is applied to compute fractal dimensions for each scene. Cumulatively, 29 scenes taken from 1992, 111 scenes taken from 1993, 110 scenes from 1994, 98 scenes taken from 1995 and 38 scenes taken from 1996 are analyzed. The spatial resolution of each scene is two degrees along both longitudinal and latitudinal directions. The annual averages of fractal dimensions are 2.528, 2.527, 2.523, 2.523 and 2.524 for 1992, 1993, 1994, 1995 and 1996, respectively. # 1999 Elsevier Science Ltd. All rights reserved.
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The fractal properties of Sea Surface Topography derived from TOPEX/POSEIDON (1992–1996)
Computers & Geosciences, 1999Co-Authors: Tian-yuan Shih, Jin-tsong Hwang, Tzong-jer TsaiAbstract:Fractal dimension with various algorithms has increasing applications in characterizing both linear and areal features. In this study, the variabilities of Sea Surface Topography derived from TOPEX/POSEIDON are studied. The variogram method is applied to compute fractal dimensions for each scene. Cumulatively, 29 scenes taken from 1992, 111 scenes taken from 1993, 110 scenes from 1994, 98 scenes taken from 1995 and 38 scenes taken from 1996 are analyzed. The spatial resolution of each scene is two degrees along both longitudinal and latitudinal directions. The annual averages of fractal dimensions are 2.528, 2.527, 2.523, 2.523 and 2.524 for 1992, 1993, 1994, 1995 and 1996, respectively. # 1999 Elsevier Science Ltd. All rights reserved.
Chester J Koblinsky - One of the best experts on this subject based on the ideXlab platform.
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an error covariance model for Sea Surface Topography and velocity derived from topex poseidon altimetry
Journal of Geophysical Research, 1994Co-Authors: Lucia S Tsaoussi, Chester J KoblinskyAbstract:In order to facilitate the use of satellite altimeter-derived Sea Surface Topography and velocity in oceanographic models, a methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The Topography and velocity are modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, Surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON Topography relative to the geoid for one 10-day period is found to be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the Topography is 3.5 cm RMS. This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions; they are less than 2 cm/s over most of the Southern Ocean. For both variables the largest errors are caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from reSearch with TOPEX/POSEIDON data. Consequently, estimates of the time dependent Sea Surface Topography from TOPEX/POSEIDON could achieve a total uncertainty of less than 3 cm RMS. This level of accuracy from a spaceborne sensor represents a remarkable engineering achievement and a major contribution to ocean science.
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An error covariance model for Sea Surface Topography and velocity derived from TOPEX/POSEIDON Altimetry
Journal of Geophysical Research, 1994Co-Authors: Lucia S Tsaoussi, Chester J KoblinskyAbstract:In order to facilitate the use of satellite altimeter-derived Sea Surface Topography and velocity in oceanographic models, a methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The Topography and velocity are modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, Surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON Topography relative to the geoid for one 10-day period is found to be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the Topography is 3.5 cm RMS. This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions; they are less than 2 cm/s over most of the Southern Ocean. For both variables the largest errors are caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from reSearch with TOPEX/POSEIDON data. Consequently, estimates of the time dependent Sea Surface Topography from TOPEX/POSEIDON could achieve a total uncertainty of less than 3 cm RMS. This level of accuracy from a spaceborne sensor represents a remarkable engineering achievement and a major contribution to ocean science.
Ilias N. Tziavos - One of the best experts on this subject based on the ideXlab platform.
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On the combined adjustment of tide gauge, marine geoid and Sea Surface Topography towards the unification of the Greek vertical datum
2010Co-Authors: Georgios Vergos, Ilias N. TziavosAbstract:Countries like Greece with extensive coastlines and a large number of islands, usually suffer from the absence of a common, for the entire country, unified vertical reference system. This holds not only for the islands, where hydrostatic leveling has not been applied, but also for distant parts of the country where trigonometric and leveling benchmarks are not tied to the country’s vertical zero, but to a local one usually coinciding with a local tide gauge station. Especially for Greece, no effort has been made until today for a common adjustment of all tide gauge data and for the unification of the country’s vertical datum. The present work focuses on the utilization of available tide gauge and spirit leveling data with computed marine geoid and Sea Surface Topography models, towards the determination of a common corrector Surface for continental and insular Greece as well as the unification of the country’s vertical datum. The aforementioned corrector Surface provides correction values to be applied to local tide gauge data, so that the local zero height will coincide with that at the origin of the vertical system. The concept is based on a common adjustment of the available data in a parametric scheme imposing a condition concerning the value of the corrector model at the existing vertical origin of the country. The necessary observation equations are outlined together with the theoretical concepts of the data combination scheme. Various reference Surfaces are investigated and validated against each other and in terms of the prediction error they provide. The results of this work successfully manage to provide correction values for the entire country, so that local heights tied to a local tide gauge station can be referred to the initial point of the country’s vertical datum.
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Geoid and high resolution Sea Surface Topography modelling in the mediterranean from gravimetry, altimetry and GOCE data: evaluation by simulation
Journal of Geodesy, 2008Co-Authors: Riccardo Barzaghi, Ilias N. Tziavos, N. Tselfes, Georgios VergosAbstract:The determination of local geoid models has traditionally been carried out on land and at Sea using gravity anomaly and satellite altimetry data, while it will be aided by the data expected from satellite missions such as those from the Gravity field and steady-state ocean circulation explorer (GOCE). To assess the performance of heterogeneous data combination to local geoid determination, simulated data for the central Mediterranean Sea are analyzed. These data include marine and land gravity anomalies, altimetric Sea Surface heights, and GOCE observations processed with the space-wise approach. A spectral analysis of the aforementioned data shows their complementary character. GOCE data cover long wavelengths and account for the lack of such information from gravity anomalies. This is exploited for the estimation of local covariance function models, where it is seen that models computed with GOCE data and gravity anomaly empirical covariance functions perform better than models computed without GOCE data. The geoid is estimated by different data combinations and the results show that GOCE data improve the solutions for areas covered poorly with other data types, while also accounting for any long wavelength errors of the adopted reference model that exist even when the ground gravity data are dense. At Sea, the altimetric data provide the dominant geoid information. However, the geoid accuracy is sensitive to orbit calibration errors and unmodeled Sea Surface Topography (SST) effects. If such effects are present, the combination of GOCE and gravity anomaly data can improve the geoid accuracy. The present work also presents results from simulations for the recovery of the stationary SST, which show that the combination of geoid heights obtained from a spherical harmonic geopotential model derived from GOCE with satellite altimetry data can provide SST models with some centimeters of error. However, combining data from GOCE with gravity anomalies in a collocation approach can result in the estimation of a higher resolution geoid, more suitable for high resolution mean dynamic SST modeling. Such simulations can be performed toward the development and evaluation of SST recovery methods.
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Quasi-stationary Sea Surface Topography estimation by the multiple input/output method
Journal of Geodesy, 2001Co-Authors: V. D. Andritsanos, Michael G. Sideris, Ilias N. TziavosAbstract:Multiple input/multiple output system theory (MIMOST) is briefly presented, and the application of the method to the quasi-stationary Sea Surface Topography (QSST) estimation and the filtering of the input observations are discussed. The repeat character of satellite altimetry missions provides more than one sample of the measured Sea Surface height (SSH) field, and an approximation of the input signal and error power spectral densities can be determined using this successive information. A case study in the Labrador Sea is considered using SSHs from ERS1 phases C and G, ERS1-GM, ERS2 phase A and TOPEX/POSEIDON altimetric missions in combination with shipborne gravity anomalies. The time period of the observations in this study is from 1993 to 1998. Some comparisons between the techniques used for the power spectral density approximation are carried out and some remarks on the properties of the estimated QSST are presented.
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Combination of multi-satellite altimetry data with CHAMP and GRACE EGMs for geoid and Sea Surface Topography determination
Dynamic Planet, 1Co-Authors: Georgios Vergos, Vassilios Grigoriadis, Ilias N. Tziavos, Michael G. SiderisAbstract:Since the launch of the first altimetric missions a wealth of data for the Sea Surface has become available and utilized for geoid and Sea Surface Topography modeling. The data from the gravity field dedicated satellite missions of CHAMP and GRACE provide a unique opportunity for combination studies with satellite altimetric observations. This study focuses on the combination of data from GEOSAT, ERS1/2, Topex/Poseidon, JASON-1 and ENVISAT with Earth Gravity Models (EGMs) generated from CHAMP and GRACE data to study the mean Sea Surface (MSS)/marine geoid in the Mediterranean Sea. Various combination methods, i.e., weighted least squares and least squares collocation are investigated and conclusions on the most appropriate combination strategy are drawn. Then, a remove-compute-restore scheme is followed to estimate the MSS model. Comparisons with other MSS models referenced to EGM96 and CHAMP/GRACE EGMs are performed in terms of the geoid height values at various control points. Finally, a Sea Surface Topography model for the eastern part of the Mediterranean Sea is determined by a combination of the altimetric geoid and the CHAMP/GRACE EGM. The latteris validated against a Sea Surface Topography model derived from altimetric data, in-situ oceanographic observations and an ocean general circulation model.
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On the incorporation of Sea Surface Topography in establishing vertical control
International Association of Geodesy Symposia, 1Co-Authors: Georgia Fotopoulos, Ilias N. Tziavos, Michael G. SiderisAbstract:One of the major sources of distortion in vertical control networks is caused by neglecting Sea Surface Topography (SST) at tide gauge stations. Often, the orthometric height is fixed to zero at these stations without applying proper corrections for the deviation of the mean Sea Surface from the equipotential Surface represented by the geoid. In view of the significant improvements in SST determination made in the past decade (particularly the low-to-medium frequencies) and the expected improvement in global gravity field models in the near future, it is appropriate to consider practical methods for the incorporation of SST into establishing vertical control. The purpose of this paper is to develop a consistent procedure for incorporating the mean SST values into the combined height network adjustment of terrestrial GPS-on-benchmark data and GPS-on-tide gauge data typically located in coastal areas, harbours, estuaries and/or river mouths. Two main issues that arise for the proper incorporation of SST information into the optimal heterogeneous height network adjustment include (i) the modelling of systematic errors and datum discrepancies among the height data types (ellipsoidal, orthometric, geoid and SST) using a corrector Surface and (ii) the separation of random errors for estimating variance components for each height type. The limiting factor in all of these studies is data availability or rather lack of quality data and obtaining reliable initial covariance matrices for the height data in a particular region. However, in lieu of the increased need for cm-level accurate vertical control it is expected that this situation will be significantly improved in the near future.
Tian-yuan Shih - One of the best experts on this subject based on the ideXlab platform.
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the fractal properties of Sea Surface Topography derived from topex poseidon 1992 1996
Computers & Geosciences, 1999Co-Authors: Tian-yuan Shih, Jin-tsong Hwang, Tzong-jer TsaiAbstract:Fractal dimension with various algorithms has increasing applications in characterizing both linear and areal features. In this study, the variabilities of Sea Surface Topography derived from TOPEX/POSEIDON are studied. The variogram method is applied to compute fractal dimensions for each scene. Cumulatively, 29 scenes taken from 1992, 111 scenes taken from 1993, 110 scenes from 1994, 98 scenes taken from 1995 and 38 scenes taken from 1996 are analyzed. The spatial resolution of each scene is two degrees along both longitudinal and latitudinal directions. The annual averages of fractal dimensions are 2.528, 2.527, 2.523, 2.523 and 2.524 for 1992, 1993, 1994, 1995 and 1996, respectively. # 1999 Elsevier Science Ltd. All rights reserved.
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The fractal properties of Sea Surface Topography derived from TOPEX/POSEIDON (1992–1996)
Computers & Geosciences, 1999Co-Authors: Tian-yuan Shih, Jin-tsong Hwang, Tzong-jer TsaiAbstract:Fractal dimension with various algorithms has increasing applications in characterizing both linear and areal features. In this study, the variabilities of Sea Surface Topography derived from TOPEX/POSEIDON are studied. The variogram method is applied to compute fractal dimensions for each scene. Cumulatively, 29 scenes taken from 1992, 111 scenes taken from 1993, 110 scenes from 1994, 98 scenes taken from 1995 and 38 scenes taken from 1996 are analyzed. The spatial resolution of each scene is two degrees along both longitudinal and latitudinal directions. The annual averages of fractal dimensions are 2.528, 2.527, 2.523, 2.523 and 2.524 for 1992, 1993, 1994, 1995 and 1996, respectively. # 1999 Elsevier Science Ltd. All rights reserved.
Lucia S Tsaoussi - One of the best experts on this subject based on the ideXlab platform.
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an error covariance model for Sea Surface Topography and velocity derived from topex poseidon altimetry
Journal of Geophysical Research, 1994Co-Authors: Lucia S Tsaoussi, Chester J KoblinskyAbstract:In order to facilitate the use of satellite altimeter-derived Sea Surface Topography and velocity in oceanographic models, a methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The Topography and velocity are modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, Surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON Topography relative to the geoid for one 10-day period is found to be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the Topography is 3.5 cm RMS. This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions; they are less than 2 cm/s over most of the Southern Ocean. For both variables the largest errors are caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from reSearch with TOPEX/POSEIDON data. Consequently, estimates of the time dependent Sea Surface Topography from TOPEX/POSEIDON could achieve a total uncertainty of less than 3 cm RMS. This level of accuracy from a spaceborne sensor represents a remarkable engineering achievement and a major contribution to ocean science.
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An error covariance model for Sea Surface Topography and velocity derived from TOPEX/POSEIDON Altimetry
Journal of Geophysical Research, 1994Co-Authors: Lucia S Tsaoussi, Chester J KoblinskyAbstract:In order to facilitate the use of satellite altimeter-derived Sea Surface Topography and velocity in oceanographic models, a methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The Topography and velocity are modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, Surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON Topography relative to the geoid for one 10-day period is found to be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the Topography is 3.5 cm RMS. This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions; they are less than 2 cm/s over most of the Southern Ocean. For both variables the largest errors are caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from reSearch with TOPEX/POSEIDON data. Consequently, estimates of the time dependent Sea Surface Topography from TOPEX/POSEIDON could achieve a total uncertainty of less than 3 cm RMS. This level of accuracy from a spaceborne sensor represents a remarkable engineering achievement and a major contribution to ocean science.