Christopher Jekeli

Bio: Christopher Jekeli is an academic researcher from Ohio State University. The author has contributed to research in topics: Gravitational field & Geoid. The author has an hindex of 30, co-authored 100 publications receiving 2947 citations. Previous affiliations of Christopher Jekeli include Phillips Laboratory.

Inertial navigation systems with geodetic applications

Abstract: Coordinate frames and transformations ordinary differential equations inertial measurement unit inertial navigation system system error dynamics stochastic processes and error models linear estimation INS initialization and alignment the global positioning system (GPS) geodetic application.

The determination of gravitational potential differences from satellite-to-satellite tracking

Abstract: A new, rigorous model is developed for the difference of gravitational potential between two close earth-orbiting satellites in terms of measured range-rates, velocities and velocity differ- ences, and specific forces It is particularly suited to regional geopotential determination from a satellite-to-satellite tracking mission Based on energy considerations, the model specifically ac- counts for the time variability of the potential in inertial space, principally due to earth's rotation Analysis shows the latter to be a significant ( 1m 2 /s 2 ) effect that overshadows by many orders of magnitude other time dependencies caused by solar and lunar tidal potentials Also, variations in earth rotation with respect to terrestrial and celestial coordinate frames are inconsequential Results of simulations contrast the new model to the simplified linear model (relating potential difference to range-rate) and delineate accuracy requirements in velocity vector measurements needed to supple- ment the range-rate measurements The numerical analysis is oriented toward the scheduled Gravity Recovery and Climate Experiment (GRACE) mission and shows that an accuracy in the velocity difference vector of 2 10 5 m/s would be commensurate within the model to the anticipated accuracy of 10 6 m/s in range-rate

Non-isotropic filtering of GRACE temporal gravity for geophysical signal enhancement

Abstract: SUMMARY Monthly mass variations within the Earth system produce temporal gravity changes, which are observable by the NASA/GFZ Gravity Recovery and Climate Experiment (GRACE) twin-satellite system. Mass load changes with spatial scales larger than 1000 km have been observed using conventional filters based on a Gaussian smoother, which applies a weight to GRACE spherical harmonic (SH) coefficients depending only on SH degree. This practice is consistent with a degree-dependent error model for GRACE monthly geopotential solutions. The Gaussian filters effectively dampen all power of ill-determined higher-degree components in the estimates. However, the spatial sampling provided by GRACE yields errors that vary with both SH degree and order. The consequence is that maps of spatial loads shall not be smoothed with an isotropic (degree-only) filter, but shall be constructed using anisotropic smoothing thus also yielding better spatial resolution in latitude. We have developed a non-isotropic filter to optimize the smoothing of GRACE temporal gravity observations by considering the degree- and order-dependent quality of GRACE estimates, the latter analysed from the correlation with the predicted signals of hydrologic and ocean models. In order to retain GRACE coefficients in the filtering process that show reasonable correlation with the geophysical (hydrology and ocean) models, we applied Gaussian-type smoothing but with averaging radius depending on the order of the geopotential coefficient estimates. Applied to 2 yr of GRACE data, we showed that the resulting non-isotropic filter yields enhanced GRACE signals with significantly higher resolution in latitude and the same resolution in longitude without reducing the accuracy as compared to the conventional Gaussian smoother.

Time-variable aliasing effects of ocean tides, atmosphere, and continental water mass on monthly mean GRACE gravity field

Abstract: [1] The Gravity Recovery and Climate Experiment (GRACE) satellite mission will provide new measurements of Earth's static and time-variable gravity fields with monthly resolution. The temporal effects due to ocean tides and atmospheric mass redistribution are assumed known and could be removed using current models. In this study we quantify the aliasing effects on monthly mean GRACE gravity estimates due to errors in models for ocean tides and atmosphere and due to ground surface water mass variation. Our results are based on simulations of GRACE recovery of monthly gravity solution complete to degree and order 120 in the presence of the respective model errors and temporal aliasing effects. For ocean tides we find that a model error in S2 causes errors 3 times larger than the measurement noise at n < 15 in the monthly gravity solution. Errors in K1, O1, and M2 can be reduced to below the measurement noise level by monthly averaging. For the atmosphere, model errors alias the solution at the measurement noise level. The errors corrupt recovered coefficients and introduce 30% more error in the global monthly geoid estimates up to maximum degree 120. Assuming daily CDAS-1 data for continental surface water mass redistribution, the analysis indicates that the daily soil moisture and snow depth variations with respect to their monthly mean produce a systematic error as large as the measurement noise over the continental regions.

An analysis of vertical deflections derived from high-degree spherical harmonic models

Abstract: The theoretical differences between the Helmert deflection of the vertical and that computed from a truncated spherical harmonic series of the gravity field, aside from the limited spectral content in the latter, include the curvature of the normal plumb line, the permanent tidal effect, and datum origin and orientation offsets. A numerical comparison between deflections derived from spherical harmonic model EGM96 and astronomic deflections in the conterminous United States (CONUS) shows that correcting these systematic effects reduces the mean differences in some areas. Overall, the mean difference in CONUS is reduced from −0.219 arcsec to −0.058 arcsec for the south–north deflection, and from +0.016 arcsec to +0.004 arcsec for the west–east deflection. Further analysis of the root-mean-square differences indicates that the high-degree spectrum of the EGM96 model has significantly less power than implied by the deflection data.

The development and evaluation of the Earth Gravitational Model 2008 (EGM2008)

Abstract: [1] EGM2008 is a spherical harmonic model of the Earth's gravitational potential, developed by a least squares combination of the ITG-GRACE03S gravitational model and its associated error covariance matrix, with the gravitational information obtained from a global set of area-mean free-air gravity anomalies defined on a 5 arc-minute equiangular grid This grid was formed by merging terrestrial, altimetry-derived, and airborne gravity data Over areas where only lower resolution gravity data were available, their spectral content was supplemented with gravitational information implied by the topography EGM2008 is complete to degree and order 2159, and contains additional coefficients up to degree 2190 and order 2159 Over areas covered with high quality gravity data, the discrepancies between EGM2008 geoid undulations and independent GPS/Leveling values are on the order of ±5 to ±10 cm EGM2008 vertical deflections over USA and Australia are within ±11 to ±13 arc-seconds of independent astrogeodetic values These results indicate that EGM2008 performs comparably with contemporary detailed regional geoid models EGM2008 performs equally well with other GRACE-based gravitational models in orbit computations Over EGM96, EGM2008 represents improvement by a factor of six in resolution, and by factors of three to six in accuracy, depending on gravitational quantity and geographic area EGM2008 represents a milestone and a new paradigm in global gravity field modeling, by demonstrating for the first time ever, that given accurate and detailed gravimetric data, asingle global model may satisfy the requirements of a very wide range of applications

Post‐processing removal of correlated errors in GRACE data

Abstract: [1] Gravity fields produced by the Gravity Recovery and Climate Experiment (GRACE) satellite mission require smoothing to reduce the effects of errors present in short wavelength components. As the smoothing radius decreases, these errors manifest themselves in maps of surface mass variability as long, linear features generally oriented north to south (i.e., stripes). The presence of stripes implies correlations in the gravity field coefficients. Here we examine the spectral signature of these correlated errors, and present a method to remove them. Finally, we apply the filter to a model of surface-mass variability to show that the filter has relatively little degradation of the underlying geophysical signals we seek to recover.

Measuring surface water from space

Abstract: [1] Surface fresh water is essential for life, yet we have surprisingly poor knowledge of the spatial and temporal dynamics of surface freshwater discharge and changes in storage globally. For example, we are unable to answer such basic questions as “What is the spatial and temporal variability of water stored on and near the surface of all continents?” Furthermore, key societal issues, such as the susceptibility of life to flood hazards, cannot be answered with the current global, in situ networks designed to observe river discharge at points but not flood events. The measurements required to answer these hydrologic questions are surface water area, the elevation of the water surface (h), its slope (∂h/∂x), and temporal change (∂h/∂t). Advances in remote sensing hydrology, particularly over the past 10 years and even more recently, have demonstrated that these hydraulic variables can be measured reliably from orbiting platforms. Measurements of inundated area have been used to varying degrees of accuracy as proxies for discharge but are successful only when in situ data are available for calibration; they fail to indicate the dynamic topography of water surfaces. Radar altimeters have a rich, multidecadal history of successfully measuring elevations of the ocean surface and are now also accepted as capable tools for measuring h along orbital profiles crossing freshwater bodies. However, altimeters are profiling tools, which, because of their orbital spacings, miss too many freshwater bodies to be useful hydrologically. High spatial resolution images of ∂h/∂t have been observed with interferometric synthetic aperture radar, but the method requires emergent vegetation to scatter radar pulses back to the receiving antenna. Essentially, existing spaceborne methods have been used to measure components of surface water hydraulics, but none of the technologies can singularly supply the water volume and hydraulic measurements that are needed to accurately model the water cycle and to guide water management practices. Instead, a combined imaging and elevation-measuring approach is ideal as demonstrated by the Shuttle Radar Topography Mission (SRTM), which collected images of h at a high spatial resolution (∼90 m) thus permitting the calculation of ∂h/∂x. We suggest that a future satellite concept, the Water and Terrestrial Elevation Recovery mission, will improve upon the SRTM design to permit multitemporal mappings of h across the world's wetlands, floodplains, lakes, reservoirs, and rivers.

Estimating groundwater storage changes in the Mississippi River basin (USA) using GRACE

Abstract: Based on satellite observations of Earth’s time variable gravity field from the Gravity Recovery and Climate Experiment (GRACE), it is possible to derive variations in terrestrial water storage, which includes groundwater, soil moisture, and snow. Given auxiliary information on the latter two, one can estimate groundwater storage variations. GRACE may be the only hope for groundwater depletion assessments in data-poor regions of the world. In this study, soil moisture and snow were simulated by the Global Land Data Assimilation System (GLDAS) and used to isolate groundwater storage anomalies from GRACE water storage data for the Mississippi River basin and its four major sub-basins. Results were evaluated using water level records from 58 wells set in the unconfined aquifers of the basin. Uncertainty in the technique was also assessed. The GRACE-GLDAS estimates compared favorably with the well based time series for the Mississippi River basin and the two sub-basins that are larger than 900,000 km2. The technique performed poorly for the two sub-basins that have areas of approximately 500,000 km2. Continuing enhancement of the GRACE processing methods is likely to improve the skill of the technique in the future, while also increasing the temporal resolution.

In-Car Positioning and Navigation Technologies—A Survey

Abstract: In-car positioning and navigation has been a killer application for Global Positioning System (GPS) receivers, and a variety of electronics for consumers and professionals have been launched on a large scale. Positioning technologies based on stand-alone GPS receivers are vulnerable and, thus, have to be supported by additional information sources to obtain the desired accuracy, integrity, availability, and continuity of service. A survey of the information sources and information fusion technologies used in current in-car navigation systems is presented. The pros and cons of the four commonly used information sources, namely, 1) receivers for radio-based positioning using satellites, 2) vehicle motion sensors, 3) vehicle models, and 4) digital map information, are described. Common filters to combine the information from the various sources are discussed. The expansion of the number of satellites and the number of satellite systems, with their usage of available radio spectrum, is an enabler for further development, in combination with the rapid development of microelectromechanical inertial sensors and refined digital maps.