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NASA NTRS1987

Zonal winds near Venus' cloud top level - A model study of the interaction between the zonal mean circulation and the semidiurnal tide

The Holton (1982) wave-mean flow interaction model's primitive equation is presently adapted in order to clarify the interaction between the semidiurnal tide and the thermally driven mean meridional circulation near cloud top level. The model is found to produce midlatitude jets whose structure is insensitive to vertical shear of the background angular velocity, both above and below cloud top level; a sensitivity to background angular velocity at cloud top level, however, is noted. Agreement between the model tide and either the observed one or that generated by the more detailed calculations of Pechmann and Ingersoll (1984) is found to be greatest when the background angular velocity at the jet level is of the order of 30 percent larger than that which is observed.

Baker, Nancy L.↗

NASA NTRS1990

Long-range sound propagation: A review of some experimental data

Three experimental studies of long range sound propagation carried out or sponsored in the past by NASA are briefly reviewed to provide a partial prospective for some of the analytical studies presented in this symposium. The three studies reviewed cover (1) a unique test of two large rocket engines conducted in such a way as to provide an indication of possible atmospheric scattering loss from a large low-frequency directive sound source, (2) a year-long measurement of low frequency sound propagation which clearly demonstrated the dominant influence of the vertical gradient in the vector sound velocity towards the receiver in defining excess sound attenuation due to refraction, and (3), a series of excess ground attenuation measurements over grass and asphalt surfaces replicated several times under very similar inversion weather conditions.

Sutherland, Louis C.↗

NASA NTRS1992

Hydrogen leak detection in the Space Shuttle

This study focuses on a helium gas jet flowing into room air. Measurements of helium concentration and velocity in the jet-air mixture are reported. The objective is to learn about jet characteristics so that dynamically similar hydrogen leaks may be located in the Space Shuttle. The hazardous gas detection system (HGDS) in the mobile launch pad uses mass spectrometers to monitor the shuttle environment for leaks. The mass spectrometers are fed by long sample tubes which draw gas from the payload bay, mid body, aft engine compartment and external tank. The overall purpose of this study is to improve the HGDS especially in its potential for locating hydrogen leaks. A rapid-response leak detection experiment was designed, built, and tested, following on the work done in this program last summer. The apparatus included a Perkin Elmer MGA-1200 mass spectrometer and air velocity transducer, both monitored by a Macintosh IIFX computer using LabVIEW software. A jet of helium flowing into the lab air simulated a gas leak. Steady helium or hydrogen-nitrogen jets were logged for concentration and velocity, and the power spectral density of each was computed. Last year, large eddies and vortices were visually seen with Schlieren imaging, and they were detected in the time plots of the various instruments. The response time of the MGA-1200 was found in the range of 0.05 to 0.1 sec. Pulsed concentration waves were clearly detected at 25 cycles per sec by spectral analysis of MGA data. No peaks were detected in the power spectrum, so in the present study, 10 Hz bandwidth-averaged power levels were examined at regular frequency intervals. The practical consequences of last year's study are as follows: sampling frequency should be increased above the present rate of 1 sample per second so that transients could be observed and analyzed with frequency response methods. Many more experiments and conditions were observed in this second summer, including the effects of orifice diameter, jet velocity, sample tube design, radial effects, vertical flow, and low hydrogen concentrations (1 percent). A frequent observation was that the power spectrum, calculated from the Fourier transform of concentration fluctuations, gives a separate piece of information from concentration. Many of the tests suggest that power is high where mixing occurs at the helium-air interface. This fact is apparently independent of the concentration level, which could be high or low, but depends on the sample location relative to the jet (leak) origin, whereas high concentration may be due to a strong leak far away or a small leak close to the sample tube. If the power is low for any concentration level, this would signify helium is arriving at the sample tube by diffusion, not chaotic mixing caused by the jet interaction with air. The practical result is to propose a modification of the HGDL mass spectrometer data sampling and software so that sampling rates could be capable of observing at least 25 Hz fluctuations.

Barile, Ronald G↗

NASA NTRS1994

Shortwave feedbacks and El Nino-Southern Oscillation: Forced ocean coupled ocean-atmosphere experiments

Changes in tropical sea surface temperature (SST) can produce changes in cloudiness that modify incoming solar shortwave (SW) radiation, which in turn affects SST. The effects of this negative feedback on Pacific interannual variability are examined in forced ocean model and hybrid coupled ocean-atmosphere model simulations. Two empirical schemes are used to model the large-scale, low-frequency response of surface SW to SST anomalies. The first scheme attempts to account for the nonlocal nature of the atmospheric response to SST based patterns of covariability analyzed through singular value decomposition. In the observations the primary coupled mode of variability is composed of a SW anomaly in the central Pacific that covaries with anomalous SST in the eastern Pacific. This is applied in the model as a nonlocal feedback. The second scheme examines the effects of a purely local feedback with a spatially varying coefficient of magnitude chosen similar to the first scheme. In almost all cases the second scheme behaved similarly to the first, presumably because the correlation scale of SST is large enough for El Nino-Southern Oscillation (ENSO) dynamics that there is little sensitivity to the local approximation in the SW feedback. In simulations forced by time series of observed wind stress the SW feedback induced very minor SST damping. Results for a simpified heat budget analysis showed that while the SW feedback increased the local heat flux damping on SST, it also induced a mean shallowing of the mixed layer. The resulting changes in both the local mean vertical temperature gradient and the zonal velocity response to the wind stress acted to oppose the local heat flux damping effects. When the observed SW anomalies were applied to forced simulations, the simulated SST anomalies were modified as expected, and agreement with observed SST improved. In coupled simulations the SW feedbacks had greater impact than in the case of specified stress. The main effects were to decrease the magnitude of the warm and cold SST anomalies in the central Pacific, while leaving the pattern and evolution of ENSO anomalies essentially unchanged elsewhere. The SW feedbacks thus produce a modest improvement of the model ENSO SST pattern compared with observations, although they tended to shorten the period of the model ENSO cycle. Overall the results suggest that large-scale SW feedbacks are of quantitative importance to simulating some aspects of the ENSO cycle but are not critical to the overall occurrence of the phenomenon.

Waliser, Duane E.↗

NASA NTRS2003

Conceptual design of a geostationary radar for hurricane studies

A novel 35-GHz Doppler radar instrument concept and the associated critical technologies are being developed for detailed monitoring of hurricanes and severe storms from a geostationary orbit. This instrument is designed to make quantitative rainfall rate profiling measurements at 13-km horizontal resolution and 300-m vertical resolution, and the radial Doppler velocity at 0.3 m/s precision, of the 3-D hurricane structure once per hour throughout its life cycle.

precipitation↗

NASA NTRS2012

Evaluation of Cloud Microphysics Simulated using a Meso-Scale Model Coupled with a Spectral Bin Microphysical Scheme through Comparison with Observation Data by Ship-Borne Doppler and Space-Borne W-Band Radars

Equivalent radar reflectivity factors (Ze) measured by W-band radars are directly compared with the corresponding values calculated from a three-dimensional non-hydrostatic meso-scale model coupled with a spectral-bin-microphysical (SBM) scheme for cloud. Three case studies are the objects of this research: one targets a part of ship-borne observation using 95 GHz Doppler radar over the Pacific Ocean near Japan in May 2001; other two are aimed at two short segments of space-borne observation by the cloud profiling radar on CloudSat in November 2006. The numerical weather prediction (NWP) simulations reproduce general features of vertical structures of Ze and Doppler velocity. A main problem in the reproducibility is an overestimation of Ze in ice cloud layers. A frequency analysis shows a strong correlation between ice water contents (IWC) and Ze in the simulation; this characteristic is similar to those shown in prior on-site studies. From comparing with the empirical correlations by the prior studies, the simulated Ze is overestimated than the corresponding values in the studies at the same IWC. Whereas the comparison of Doppler velocities suggests that large-size snowflakes are necessary for producing large velocities under the freezing level and hence rules out the possibility that an overestimation of snow size causes the overestimation of Ze. Based on the results of several sensitivity tests, we conclude that the source of the overestimation is a bias in the microphysical calculation of Ze or an overestimation of IWC. To identify the source of the problems needs further validation research with other follow-up observations.

Iguchi, T.↗

NASA NTRS2017

Low Pressure Flame Blowoff from the Forward Stagnation Region of a Blunt-Nosed Cast PMMA Cylinder in Axial Mixed Convective Flow

Low-pressure blowoff experiments were conducted with a stagnation flame stabilized on the forward tip of cast PMMA rods in a vertical wind tunnel. Pressure, forced flow velocity, gravity, and ambient oxygen concentration were varied. Stagnation flame blowoff is determined from a time-stamped video recording of the test. The blowoff pressure is determined from test section pressure transducer data that is synchronized with the time stamp. The forced flow velocity is also determined from the choked flow orifice pressure. Most of the tests were performed in normal gravity, but a handful of microgravity tests were also conducted to determine the influence of buoyant flow velocity on the blowoff limits. The blowoff limits are found to have a linear dependence between the partial pressure of oxygen and the total pressure, regardless of forced flow velocity and gravity level. The flow velocity (forced and/or buoyant) affects the blowoff pressure through the critical Damkohler number residence time, which dictates the partial pressure of oxygen at blowoff. This is because the critical stretch rate increases linearly with increasing pressure at low pressure (sub-atmospheric pressures) since a second-order overall reaction rate with two-body reactions dominates in this pressure range.

flammability↗

DOE OSTI2023

High-fidelity Experiments of Turbulent Buoyant Jets from Simultaneous Particle Image Velocimetry and Laser Induced Fluorescence

Accurate models of turbulent buoyant flows are essential for the design of nuclear reactors thermal hydraulics and passive safety systems. However, available models fail to fully capture the physics of turbulent mixing when buoyancy becomes predominant with respect to momentum. Therefore, high-fidelity experiments of well-controlled fundamental flows are needed to develop and validate more accurate models. We performed experiments of positive and negative turbulent buoyant jets, both in uniform and stratified environments, with the aim of understanding the thermal hydraulics of turbulent mixing with variable density and providing high-fidelity data for the development and validation of turbulence models. Non-intrusive, simultaneous Particle Image Velocimetry and Laser Induced Fluorescence measurements were carried out to acquire instantaneous velocity and concentration fields on a vertical section parallel to the axis of a jet in the self-similar region. The Refractive Index Matching method was applied to measure high-resolution buoyant jets with up to 8.6% density difference. These data are free of the typical errors that characterize optical measurements of buoyancy driven flows (e.g., natural and mixed convection) where the refractive index of the fluid is inhomogeneous throughout the measurement domain. Turbulent statistics and entrainment of buoyant jets in uniform and stratified environments are presented. These data are compared with non-buoyant jets in uniform environment, as a reference to investigate the effects of buoyancy and stratification on turbulent mixing. The results will be used for the assessment of current turbulence models and as basis for the development of a new one that captures turbulent mixing.

42 ENGINEERING↗

NASA NTRS1982

Doppler radar echoes of lightning and precipitation at vertical incidence

Digital time series data at 16 heights within two storms were collected at vertical incidence with a 10-cm Doppler radar. On several occasions during data collection, lightning echoes were observed as increased reflectivity on an oscilloscope display. Simultaneously, lightning signals from nearby electric field change antennas were recorded on an analog recorder together with the radar echoes. Reflectivity, mean velocity, and Doppler spectra were examined by means of time series analysis for times during and after lightning discharges. Spectra from locations where lightning occurred show peaks, due to the motion of the lightning channel at the air speed. These peaks are considerably narrower than the ones due to precipitation. Besides indicating the vertical air velocity that can then be used to estimate hydrometeor-size distribution, the lightning spectra provide a convenient means to estimate the radar cross section of the channel. Subsequent to one discharge, we deduce that a rapid change in the orientation of hydrometeors occurred within the resolution volume.

Zrnic, D. S.↗

NASA NTRS2005

Evaluation of Vertically Resolved Water Winds from AIRS using Hurricane Katrina

The knowledge of wind velocity as a function of altitude is key to weather forecast improvements. The ability of hyperspectral sounders in principle to measure vertically resolved water winds, which has long been recognized, has been tested with Atmospheric Infrared Sounder (AIRS) data. AIRS retrievals of total column water above 300 mb have been correlated with the radiosonde upper-tropospheric wind velocity and moisture data. The excellent correlation is illustrated with results obtained from hurricane Katrina and from the western United States. AIRS is a hyperspectral infrared sounder in low Earth orbit. It was launched in May 2002. We illustrate the use of AIRS data for the measurement of upper tropospheric water by using the 2387/cm CO2 R-branch channel and the 1551/cm water vapor channel. The 2387/cm channel measures the temperature at 300 mb totally independent of water vapor. The weighting function of the 1551/cm channel peaks at 300 mb only under moist conditions; the peak shifts downward (higher temperature) for less water and upward (lower temperature) for more water. The difference between the brightness temperatures bt2387 and bt1551 cancels the local several degree weather related variability of the temperature and measures the component due to the water vapor at 300 mb.

Atmospheric Infrared Sounder (AIRS)↗

NASA NTRS1993

Microphysical properties of the November 26 cirrus cloud retrieved by Doppler radar/IR radiometer technique

Gaining information about cirrus cloud microphysics requires development of remote sensing techniques. In an earlier paper. Matrosov et al. (1992) proposed a method to estimate ice water path (IWP) (i.e., vertically integrated ice mass content IMC) and characteristic particle size averaged through the cloud from combined groundbased measurements of radar reflectivities and IR brightness temperatures of the downwelling thermal radiation in the transparency region of 10-12 mu m. For some applications, the vertically averaged characteristic particle sizes and IWP could be the appropriate information to use. However, vertical profiles of cloud microphysical parameters can provide a better understanding of cloud structure and development. Here we describe a further development of the previous method by Matrosov et al. (1992) for retrieving vertical profiles of cirrus particle sizes and IMC rather than their vertically averaged values. In addition to measurements of radar reflectivities, the measurements of Doppler velocities are used in the new method. This provides us with two vertical profiles of measurements to infer two vertical profiles of unknowns, i.e., particle characteristic sizes and IMC. Simultaneous measurements of the IR brightness temperatures are still needed to resolve an ambiguity in particle size-fall velocity relationships.

Matrosov, Sergey Y.↗

NASA NTRS1984

Flow improvements in the NASA Langley 4- by 7-meter tunnel circuit

The mean velocity profiles in both the horizontal and vertical planes of symmetry at specific locations throughout the tunnel circuit to identify the most promising means for improving the flow in the 4 by 7 meter wind tunnel were measured. In the base line tunnel flow surveys, the flow patterns near the end of the test section indicate a uniform mean velocity distribution. Downstream of the test section, unsymmetrical flow patterns result in low velocities along the inner walls and in flow separation along the inner wall of the diffuser upstream of the drive fan and along the outer wall of the large diffuser downstream of the drive fan. A set of trailing-edge flaps attached to the five flow-control vanes located just downstream of the first corner were installed. These flaps are successful in making the tunnel flow more symmetrical and in eliminating the regions of separation in the diffusers upstream and downstream of the drive fan. Previously announced in STAR as N84-15117

Applin, Z. T.↗

NASA NTRS2010

Initial Results of DC Electric Fields, Associated Plasma Drifts, Magnetic Fields, and Plasma Waves Observed on the C/NOFS Satellite

Initial results are presented from the Vector Electric Field Investigation (VEFI) on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite, a mission designed to understand, model, and forecast the presence of equatorial ionospheric irregularities. The VEFI instrument includes a vector DC electric field detector, a fixed-bias Langmuir probe operating in the ion saturation regime, a flux gate magnetometer, an optical lightning detector, and associated electronics including a burst memory. Compared to data obtained during more active solar conditions, the ambient DC electric fields and their associated E x B drifts are variable and somewhat weak, typically < 1 mV/m. Although average drift directions show similarities to those previously reported, eastward/outward during day and westward/downward at night, this pattern varies significantly with longitude and is not always present. Daytime vertical drifts near the magnetic equator are largest after sunrise, with smaller average velocities after noon. Little or no pre-reversal enhancement in the vertical drift near sunset is observed, attributable to the solar minimum conditions creating a much reduced neutral dynamo at the satellite altitude. The nighttime ionosphere is characterized by larger amplitude, structured electric fields, even where the plasma density appears nearly quiescent. Data from successive orbits reveal that the vertical drifts and plasma density are both clearly organized with longitude. The spread-F density depletions and corresponding electric fields that have been detected thus far have displayed a preponderance to appear between midnight and dawn. Associated with the narrow plasma depletions that are detected are broad spectra of electric field and plasma density irregularities for which a full vector set of measurements is available for detailed study. Finally, the data set includes a wide range of ELF/VLF/HF oscillations corresponding to a variety of plasma waves, in particular banded ELF hiss, whistlers, and lower hybrid wave turbulence triggered by lightning-induced sferics. The VEFI data represents a new set of measurements that are germane to numerous fundamental aspects of the electrodynamics and irregularities inherent to the Earth's low latitude ionosphere.

Pfaff, R.↗

NASA NTRS2011

DC Electric Fields, Associated Plasma Drifts, and Irregularities Observed on the C/NOFS Satellite

Results are presented from the Vector Electric Field Investigation (VEFI) on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite, a mission designed to understand, model, and forecast the presence of equatorial ionospheric irregularities. The VEFI instrument includes a vector DC electric field detector, a fixed-bias Langmuir probe operating in the ion saturation regime, a flux gate magnetometer, an optical lightning detector, and associated electronics including a burst memory. Compared to data obtained during more active solar conditions, the ambient DC electric fields and their associated E x B drifts are variable and somewhat weak, typically < 1 mV/m. Although average drift directions show similarities to those previously reported, eastward/outward during day and westward/downward at night, this pattern varies significantly with longitude and is not always present. Daytime vertical drifts near the magnetic equator are largest after sunrise, with smaller average velocities after noon. Little or no pre-reversal enhancement in the vertical drift near sunset is observed, attributable to the solar minimum conditions creating a much reduced neutral dynamo at the satellite altitude. The nighttime ionosphere is characterized by larger amplitude, structured electric fields, even where the plasma density appears nearly quiescent. Data from successive orbits reveal that the vertical drifts and plasma density are both clearly organized with longitude. The spread-F density depletions and corresponding electric fields that have been detected thus far have displayed a preponderance to appear between midnight and dawn. Associated with the narrow plasma depletions that are detected are broad spectra of electric field and plasma density irregularities for which a full vector set of measurements is available for detailed study. The VEFI data represents a new set of measurements that are germane to numerous fundamental aspects of the electrodynamics and irregularities inherent to the Earth s low latitude ionosphere.

Pfaff, R.↗

NASA NTRS2018

Finite Element Simulations of Two Vertical Drop Tests of F-28 Fuselage Sections

In March 2017, a vertical drop test of a forward fuselage section of a Fokker F-28 MK4000 aircraft was conducted as part of a joint NASA/FAA project to investigate the performance of transport aircraft under realistic crash conditions. In June 2017, a vertical drop test was conducted of a wing-box fuselage section of the same aircraft. Both sections were configured with two rows of aircraft seats, in a triple-double configuration. A total of ten Anthropomorphic Test Devices (ATDs) were secured in seats using standard lap belt restraints. The forward fuselage section was also configured with luggage in the cargo hold. Both sections were outfitted with two hat racks, each with added ballast mass. The drop tests were performed at the Landing and Impact Research facility located at NASA Langley Research Center in Hampton, Virginia. The measured impact velocity for the forward fuselage section was 346.8-in/s onto soil. The wing-box section was dropped with a downward facing pitch angle onto a sloping soil surface in order to create an induced forward acceleration in the airframe. The vertical impact velocity of the wing-box section was 349.2-in/s. A second objective of this project was to assess the capabilities of finite element simulations to predict the test responses. Finite element models of both fuselage sections were developed for execution in LS-DYNA(Registered Trademark), a commercial explicit nonlinear transient dynamic code. The models contained accurate representations of the airframe structure, the hat racks and hat rack masses, the floor and seat tracks, the luggage in the cargo hold for the forward section, and the detailed under-floor structure in the wing-box section. Initially, concentrated masses were used to represent the inertial properties of the seats, restraints, and ATD occupants. However, later simulations were performed that included finite element representations of the seats, restraints, and ATD occupants. These models were developed to more accurately replicate the seat loading of the floor and to enable prediction of occupant impact responses. Models were executed to generate analytical predictions of airframe responses, which were compared with test data to validate the model. Comparisons of predicted and experimental structural deformation and failures were made. Finally, predicted and experimental soil deformation and crater depths were also compared for both drop test configurations.

Jackson, Karen E.↗

NASA NTRS2014

Collisional Effects on Magnesium-rich Minerals found in Comets and Asteroids

While generally touted to be the least-altered bodies remaining from the age of the solar system's formation, comets and asteroids have undergone evolutionary processing throughout the 4.5-billion-year lifetime of the solar system. They have suffered the effects of collisions by impactors ranging in size from micrometeoroids to other comets and asteroids. As such, we must ask ourselves: can we detect these evolutionary effects remotely through telescopic observations? With this in mind, a suite of experiments were conducted, impacting magnesium-rich minerals as analogues to those that have been detected in the spectra of both asteroid surfaces and in the dust of cometary comae, including forsterite (Mg2SiO4, olivine), orthoenstatite (Mg2SiO3, pyroxene), diopside (MgCaSi2O6, monoclinic pyroxene), and magnesite (MgCO3, carbonate). These minerals were impacted at velocities ranging from 2.0 km/s to 2.8 km/s using the vertical gun in the Experimental Impact Laboratory (EIL) at NASA Johnson Space Center. These speeds mimic typical velocities of impacts occurring in the Kuiper belt [1]. Two classes of projectile were used: spherical alumina ceramic, whose density mimics that of rock, and cylinders made from the same material that they impacted (e.g., forsterite impactors for forsterite targets, etc.). The peak shock pressure varies significantly, depending on the target and impactor materials and the velocity; thus, shock effects differed in targets impacted at the same velocity but with compositionally different projectiles. The results indicate both: (a) how varying the impactor-density might change the outcome from a scientific viewpoint, as well as (b) possible contamination effects of the ceramic projectile in the resultant spectra of the target minerals from an experimental perspective. Temperature effects were also investigated by impacting samples at both 25 deg. and -25 deg. to: (a) probe whether the varying temperatures experienced by small bodies plays a role in the resultant spectra, and (b) constrain necessary experimental parameters. Analysis of Fourier Transform Infrared (FTIR) spectra obtained from the experimentally shocked materials shows clear indications of spectral shifts in wavelength, as well as a change in relative peak strengths of the spectral signatures at one wavelength compared with another, in all minerals except magnesite. Samples of the forsterite and orthoenstatite that displayed the spectral changes were examined with a transmission electron microscope, which revealed evidence of planar dislocations. The density of the dislocations in the experimentally shocked minerals mimicked the dislocation densities measured in both forsterite and enstatite grains recovered from Comet Wild 2 by the Stardust mission [2, 3, 4]. Further discussion on analyses of peak shock pressure and temperature-dependent effects can be found in Jensen et al., this meeting

Lederer, S.↗

NASA NTRS1976

Three velocity component, nonhomogeneous atmospheric boundary layer turbulence modeling

The vertical nonhomogeneous character of turbulence in the atmospheric boundary layer results in a non-stationary turbulence process relative to an aircraft during takeoff and landing despite the fact that the turbulence statistics can be horizontally homogeneous. The simulation of the three components of the turbulent winds which include the nonstationary aspect of atmospheric turbulence is the subject of this paper. A procedure is developed and demonstrated to generate the three components of a turbulence ramdom process field, u sub i(x,z) where x and z denote horizontal and vertical coordinates and u sub i, i = 1,2,3 are the three orthogonal components of the turbulent random field. This field satisfies any desired one point auto spectra as well as two point statistics (interlevel correlations). By use of Taylors frozen eddy hypothesis we can transform the turbulent random field into the time domain and obtain the random turbulence along an aircraft trajectory.

Perlmutter, M.↗

NASA NTRS2005

Accurate Realization of GPS Vertical Global Reference Frame

The goal of this project is to improve our current understanding of GPS error sources associated with estimates of radial velocities at global scales. An improvement in the accuracy of radial global velocities would have a very positive impact on a large number of geophysical studies of current general interest such as global sea-level and climate change, coastal hazards, glacial isostatic adjustment, atmospheric and oceanic loading, glaciology and ice mass variability, tectonic deformation and volcanic inflation, and geoid variability. A set of GPS error sources relevant to this project are those related to the combination of the positions and velocities of a set of globally distributed stations as determined &om the analysis of GPS data, including possible methods of combining and defining terrestrial reference frames. This is were our research activities during this reporting period have concentrated. During this reporting period, we have researched two topics: (1) The effect of errors on the GPS satellite antenna models (or lack thereof) on global GPS vertical position and velocity estimates; (2) The effect of reference W e definition and practice on estimates of the geocenter variations.

Elosegui, Pedro↗