Geoid Information Research Articles

Создание и обновление высотной основы топографических карт в национальной пространственной системе координат: на примере Ферганской долины

The use of high-precision technology of the global navigation satellite system (GNSS) has put forward the task of developing the methods for the creation and the use of a new national open coordinate system in the Republic of Uzbekistan. In the country, up to now the CS42 coordinate system, based on the Krasovsky ellipsoid used for geodetic works. The Baltic normal system of heights (1977), tied to the mean sea level with the zero mark of the Kronstadt tide gauge, was adopted as a height datum. Due to lack geoid information for the territory of the country determined by modern methods, the realization of a height reference datum becomes an urgent task. The results of GPS measurements usually presented in a coordinate system relative to the WGS-84 ellipsoid, and have to convert to national, local coordinate systems to solve practical problems. The horizontal GPS coordinates can directly use for computational work, but the geodetic heights have to convert to orthometric (or normal) heights for a given area using geoid information. In this work, a study was made of methods for updating the height reference datum of topographic maps at a scale of 1:200,000 using a deformation matrix between two reference coordinate systems for the territory of the Fergana Valley. To convert between geodetic and normal heights between the CS42 and WGS84 coordinate systems, a vertical deformation matrix in the GTX format of the National oceanic and Atmospheric Administration of Canada (NOAA) have created. To create a file of elevation displacements, the results of classical leveling and satellite GPS measurements have used at 144 “common” points of the entire network of the country with known coordinates in two systems. The difference between the “real” values of geodetic heights obtained from GPS measurements and “modeled” ranges from -0.13 m to 0.67 m. It has revealed that the maximum differences in heights are in the area of the Fergana basin itself and may be a consequence of both an anomalous gravitational field in this part of the territory, and an insufficient density of stations of the GPS network in the northeastern part of the area. The normal height values for the updated topographic map in WGS84 have computed using the EGM2008 high precision geopotential model. The discrepancy between the values of heights in CS42 and WGS84 is in the range of -3.93 m and 0.31 m.

The combined global gravity field model XGM2019e

XGM2019e is a combined global gravity field model represented by spheroidal harmonics up to degree and order (d/o) 5399, corresponding to a spatial resolution of 2′ (~ 4 km). As data sources, it includes the satellite model GOCO06s in the longer wavelength range up to d/o 300 combined with a ground gravity grid which also covers the shorter wavelengths. The ground data consist over land and ocean of gravity anomalies provided by courtesy of NGA (15′ resolution, identical to XGM2016) augmented with topographically derived gravity information over land (EARTH2014). Over the oceans, gravity anomalies derived from satellite altimetry are used (DTU13 with a resolution of 1′). The combination of the satellite data with the ground gravity observations is performed by using full normal equations up to d/o 719 (15′). Beyond d/o 719, a block-diagonal least squares solution is calculated for the high-resolution ground gravity data (from topography and altimetry). All calculations are performed in the spheroidal harmonic domain. In the spectral band up to d/o 719, the new model shows a slightly improved behaviour in the magnitude of a few mm RMS over land as compared to preceding models such as XGM2016, EIGEN6c4 or EGM2008 when validated with independent geoid information derived from GNSS/levelling. Over land and in the spectral range above d/o 719, the accuracy of XGM2019e marginally suffers from the sole use of topographic forward modelling, and geoid differences at GNSS/levelling stations are increased in the order of several mm RMS in well-surveyed areas, such as the US and Europe, compared to models containing real gravity data over their entire spectrum, e.g. EIGEN6c4 or EGM2008. However, GNSS/levelling validation also indicates that the performance of XGM2019e can be considered as globally more consistent and independent of existing high-resolution global models. Over the oceans, the model exhibits an enhanced performance (equal or better than preceding models), which is confirmed by comparison of the MDT’s computed from CNES/CLS 2015 mean sea surface and the high-resolution geoid models. The MDT based on XGM2019e shows fewer artefacts, particularly in the coastal regions, and fits globally better to DTU17MDT which is considered as an independent reference MDT.

Dynamic ocean topography of the northern Nordic seas: a comparison between satellite altimetry and ocean modeling

Abstract. The dynamic ocean topography (DOT) of the polar seas can be described by satellite altimetry sea surface height observations combined with geoid information as well as by ocean models. The altimetry observations are characterized by an irregular sampling and seasonal sea ice coverage complicating reliable DOT estimations. Models display various spatiotemporal resolutions but are limited to their computational and mathematical context and introduced forcing models. In the present paper, ALES+ retracked altimetry ranges and derived along-track DOT heights of ESA's Envisat and water heights of the Finite Element Sea Ice-Ocean Model (FESOM) are compared to investigate similarities and discrepancies. The goal of the present paper is to identify to what extent pattern and variability of the northern Nordic seas derived from measurements and model agree with each other, respectively. The study period covers the years 2003–2009. An assessment analysis regarding seasonal DOT variabilities shows good agreement and confirms the dominant impact of the annual signal in both datasets. A comparison based on estimated regional annual signal components shows 2–3 times stronger amplitudes of the observations but good agreement of the phase. Reducing both datasets by constant offsets and the annual signal reveals small regional residuals and highly correlated DOT time series (Pearson linear correlation coefficient of at least 0.67). The highest correlations can be found in areas that are ice-free and affected by ocean currents. However, differences are visible in sea-ice-covered shelf regions. Furthermore, remaining constant artificial elevations in the observational data can be attributed to an insufficient representation of the used geoid. In general, the comparison results in good agreement between simulated and altimetry-based descriptions of the DOT in the northern Nordic seas.

Influence of local geoid variation on water surface elevation estimates derived from multi-mission altimetry for Lake Namco

Water surface elevation (WSE) is an essential quantity for water resource monitoring and hydrodynamic modeling. Satellite altimetry has provided data for inland water bodies. The height that is derived from altimetry measurement is ellipsoidal height. In order to convert the ellipsoidal height to orthometric height, which has physical meaning, accurate estimates of the geoid are needed. This paper evaluates the suitability of geodetic altimetric measurements for improvement of global geoid models over a large lake in the Tibetan Plateau. CryoSat-2 and SARAL/AltiKa are used to derive the high-frequency geoid correction. A validation of the local geoid correction is performed with data from in-situ observations, a laser altimetry satellite (ICESat), a Ka-band radar altimetry satellite (SARAL) and a SAR radar altimetry satellite (Sentinel-3). Results indicate that the geodetic altimetric dataset can capture the high-resolution geoid information. By applying local geoid correction, the precision of ICESat, SARAL and Sentinel-3 retrievals are significantly improved. We conclude that using geodetic altimetry to correct for local geoid residual over large lakes significantly decreases the uncertainty of WSE estimates. These results also indicate the potential of geodetic altimetry missions to determine local geoid residual with centimeter-level accuracy, which can be used to improve global and regional geopotential models.

Intercontinental height datum connection with GOCE and GPS-levelling data

AbstractIn this study an attempt is made to establish height system datum connections based upon a gravity field and steady-state ocean circulation explorer (GOCE) gravity field model and a set of global positioning system (GPS) and levelling data. The procedure applied in principle is straightforward. First local geoid heights are obtained point wise from GPS and levelling data. Then the mean of these geoid heights is computed for regions nominally referring to the same height datum. Subsequently, these local mean geoid heights are compared with a mean global geoid from GOCE for the same region. This way one can identify an offset of the local to the global geoid per region. This procedure is applied to a number of regions distributed worldwide. Results show that the vertical datum offset estimates strongly depend on the nature of the omission error, i.e. the signal not represented in the GOCE model. For a smooth gravity field the commission error of GOCE, the quality of the GPS and levelling data and the averaging control the accuracy of the vertical datum offset estimates. In case the omission error does not cancel out in the mean value computation, because of a sub-optimal point distribution or a characteristic behaviour of the omitted part of the geoid signal, one needs to estimate a correction for the omission error from other sources. For areas with dense and high quality ground observations the EGM2008 global model is a good choice to estimate the omission error correction in theses cases. Relative intercontinental height datum offsets are estimated by applying this procedure between the United State of America (USA), Australia and Germany. These are compared to historical values provided in the literature and computed with the same procedure. The results obtained in this study agree on a level of 10 cm to the historical results. The changes mainly can be attributed to the new global geoid information from GOCE, rather than to the ellipsoidal heights or the levelled heights. These historical levelling data are still in use in many countries. This conclusion is supported by other results on the validation of the GOCE models.

An ocean modelling and assimilation guide to using GOCE geoid products

Abstract. We review the procedures and challenges that must be considered when using geoid data derived from the Gravity and steady-state Ocean Circulation Explorer (GOCE) mission in order to constrain the circulation and water mass representation in an ocean general circulation model. It covers the combination of the geoid information with time-mean sea level information derived from satellite altimeter data, to construct a mean dynamic topography (MDT), and considers how this complements the time-varying sea level anomaly, also available from the satellite altimeter. We particularly consider the compatibility of these different fields in their spatial scale content, their temporal representation, and in their error covariances. These considerations are very important when the resulting data are to be used to estimate ocean circulation and its corresponding errors. We describe the further steps needed for assimilating the resulting dynamic topography information into an ocean circulation model using three different operational forecasting and data assimilation systems. We look at methods used for assimilating altimeter anomaly data in the absence of a suitable geoid, and then discuss different approaches which have been tried for assimilating the additional geoid information. We review the problems that have been encountered and the lessons learned in order the help future users. Finally we present some results from the use of GRACE geoid information in the operational oceanography community and discuss the future potential gains that may be obtained from a new GOCE geoid.

Geoid and high resolution sea surface topography modelling in the mediterranean from gravimetry, altimetry and GOCE data: evaluation by simulation

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.

Interpretation of general geophysical patterns in Iran based on GRACE gradient component analysis

Only with satellites it is possible to cover the entire Earth densely with gravity field related measurements of uniform quality within a short period of time. However, due to the altitude of the satellite orbits, the signals of individual local masses are strongly damped. Based on the approach of Petrovskaya and Vershkov we determine the gravity gradient tensor directly from the spherical harmonic coefficients of the recent EIGEN-GL04C combined model of the GRACE satellite mission. Satellite gradiometry can be used as a complementary tool to gravity and geoid information in interpreting the general geophysical and geodynamical features of the Earth. Due to the high altitude of the satellite, the effects of the topography and the internal masses of the Earth are strongly damped. However, the gradiometer data, which are nothing else than the second order spatial derivatives of the gravity potential, efficiently counteract signal attenuation at the low and medium frequencies. In this article we review the procedure for estimating the gravity gradient components directly from spherical harmonics coefficients. Then we apply this method as a case study for the interpretation of possible geophysical or geodynamical patterns in Iran. We found strong correlations between the cross-components of the gravity gradient tensor and the components of the deflection of vertical, and we show that this result agrees with theory. Also, strong correlations of the gravity anomaly, geoid model and a digital elevation model were found with the diagonal elements of the gradient tensor.

Comparison of the Hungarian first order triangulation network with the national GPS network using scale and azimuth differences

While the cadastral and topographic maps tie to the classical reference systems and frames, there will be need to know the relation between the classical and GPS-based networks in a particular country. In this study we discuss the scale factor and azimuth discrepancies between the Hungarian first order triangulation and the national GPS network emphasising their practical significance.The comparison of traditional and GPS derived slope and geodesic distances as well as the comparison of the different azimuths make possible the estimation of the scale and orientation differences of the two systems without the knowledge of height and geoid information which may contain additional errors, too.The estimated −4.34 mm/km mean value reflects the significant scale difference, which is similar to the values derived in neighbour countries. The −2.51 arcsec mean azimuth difference reflects the orientation of the two system.

Two-step procedures for hybrid geoid modelling

A variety of mathematical models exist with which to combine long-wavelength geoid information from an Earth gravity model (EGM) with terrestrial gravity data. As new data become available, such as an extended or refined EGM and/or some variance–covariance information from terrestrial gravity data, this new information can be combined with a previous geoid model through a so-called hybrid estimator. The hybrid estimator is defined as a two-step estimator, which provides a solution that is a compromise between computational labour and matching of the entire data set. Some commonly used geoid modifications are compared, and several hybrid estimators are introduced. It is concluded that, in general, hybrid estimators linking the new information to old data by the least squares principle should be preferred to deterministic combinations.

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.

III: OCEAN CIRCULATION: Global Ocean Data Assimilation and Geoid Measurements

Parts of geodesy and physical oceanography are about to mature into a single modeling problem involving the simultaneous estimation of the marine geoid and the general circulation. Both fields will benefit. To this end, we present an ocean state estimation (data assimilation) framework which is designed to obtain a dynamically consistent picture of the changing ocean circulation by combining global ocean data sets of arbitrary type with a general circulation model (GCM). The impact of geoid measurements on such estimates of the ocean circulation are numerous. For the mean circulation, a precise geoid describes the reference frame for dynamical signals in altimetric sea surface height observations. For the time-varying ocean signal, changing geoid information might be a valuable new information about correcting the changing flow field on time scales from a few month to a year, but the quantitative utility of such information has not yet been demonstrated. For a consistent estimate, some knowledge of the prior error covariances of all data fields is required. The final result must be consistent with prior error estimates for the data. State estimation is thus one of the few quantitative consistency checks for new geoid measurements anticipated from forthcoming space missions. Practical quantitative methods will yield a best possible estimate of the dynamical sea surface which, when combined with satellite altimetric surfaces, will produce a best-estimate marine geoid. The anticipated accuracy and precision of such estimates raises some novel modeling error issues which have not conventionally been of concern (the Boussinesq approximation, self-attraction and loading). Model skill at very high frequencies is a major concern because of the need to de-alias the data obtained by the inevitable oceanic temporal undersampling dictated by realistic satellite orbit configurations.

Comparison of Multimission Altimetric Sea-Surface Heights with Tide Gauge Observations in the Southern Baltic Sea

One possible technique to validate the observations of altimeter missions is the comparison with sea-surface heights measured by tide gauges. In our investigation, we compared observations of the two tide gauge stations, Sassnitz and Warnemünde, which are located at the southern coast of the Baltic Sea, with sea-surface heights obtained from the altimeter missions Geosat, ERS-1, ERS-2, and TOPEX/Poseidon. For this purpose, the compared sea-surface heights were related to a common reference system and extrapolated to a common location. GPS observations, leveling data, regional geoid information, sea-surface topography, and postglacial rebound were included in the analysis. Considering the uncertainties of all model components, a more reliable estimation of the error budget (source, type, and magnitude of the errors) was performed. The obtained absolute altimeter biases are (-243 - 32) mm for Geosat, (467 - 19) mm for ERS-1, (76 - 19) mm for ERS-2, and (13 - 18) mm for TOPEX.

The CARIB97 high-resolution geoid height model for the Caribbean Sea

A 2×2 arc-minute resolution geoid model, CARIB97, has been computed covering the Caribbean Sea. The geoid undulations refer to the GRS-80 ellipsoid, centered at the ITRF94 (1996.0) origin. The geoid level is defined by adopting the gravity potential on the geoid as W0=62 636 856.88 m2/s2 and a gravity-mass constant of GM=3.986 004 418×1014 m3/s2. The geoid model was computed by applying high-frequency corrections to the Earth Gravity Model 1996 global geopotential model in a remove-compute-restore procedure. The permanent tide system of CARIB97 is non-tidal. Comparison of CARIB97 geoid heights to 31 GPS/tidal (ITRF94/local) benchmarks shows an average offset (h–H–N) of 51 cm, with an Root Mean Square (RMS) of 62 cm about the average. This represents an improvement over the use of a global geoid model for the region. However, because the measured orthometric heights (H) refer to many differing tidal datums, these comparisons are biased by localized permanent ocean dynamic topography (PODT). Therefore, we interpret the 51 cm as partially an estimate of the average PODT in the vicinity of the 31 island benchmarks. On an island-by-island basis, CARIB97 now offers the ability to analyze local datum problems which were previously unrecognized due to a lack of high-resolution geoid information in the area.

Completion of the nationwide GPS-gravimetric geoid solution for Hungary

The establishment of the Hungarian National GPS Network (OGPSH) had been completed in 1997. It is exclusively settled on the traditional horizontal network sites, no leveling benchmarks were included. The OGPSH network consists more than 1100 GPS points, but less than 30% of the sites have trustful leveled heights. Our task was to supply the remaining points with cm-accuracy heights above the geoid in a uniform system. For this purpose a technique had been developed using the GPS data and the geoid information available. A specialized geoid solution, covering the whole country was computed and used for supporting the GPS-heighting procedure.The OGG98B GPS-gravimetric geoid solution made the GPS-heighting very simple and efficient. The accuracy of the technique was extensively tested and proved to be accurate not worse than ±3 cm. Higher residuals were found only at some points, where the height information was questionable. The improved technique is planned to be used in the 3rd order leveling network in Hungary.This paper shortly summarizes the computational procedure of the GPS-gravimetric geoid and presents some results on the GPS-heighting had been performed in the OGPSH network.

GPS Coordinate Transformations and their Use in Gravimetry

Geodetic coordinates on Australian maps are referenced to the Australian Geodectic Datum 1984 (AGD84). Topographic elevations are referred to the Australian Height Datum (AHD). Conversely, GPS yields 3-D Cartesian coordinates and coordinate differences in the World Geodetic System 1984 (WGS84).The difference between coordinates of the same point on the Earth's surface varies between 150 m to 200 m over continental Australia. This study presents a method of transforming between GPS (WGS84) and AGD84 latitude, longitude and AHD. This permits GPS-aided gravity data to be integrated with other geophysical data referred to the AGD84. A new rigorous formula to simultaneously determine the latitude, free-air and slab Bouguer corrections from GPS and geoid information is derived. It is demonstrated that, if an incorrect elevation datum is used for gravimetric data reduction, a different gravity anomaly is produced.

Geoid information by wavelength

Two models describing potential coefficient behavior are used to estimate the root mean square geoid undulation by wavelength. Four wavelength types were defined: long wavelengths: l=2 to 10; intermediate wavelengths: l=11 to 100; short wavelengths: l=101 to 1000; and very short wavelengths: l=1001 to ∞. By one representation of potential coefficient behavior the intermediate wavelength geoid information was ±5.64 m, short wavelength, ±0.66 m, and the very short wavelength, ±0.05 m. The procedures of this paper were applied to an actual residual undulation computation using detailed gravity material.