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NASA NTRS2012

Geopotential Field Anomaly Continuation with Multi-Altitude Observations

Conventional gravity and magnetic anomaly continuation invokes the standard Poisson boundary condition of a zero anomaly at an infinite vertical distance from the observation surface. This simple continuation is limited, however, where multiple altitude slices of the anomaly field have been observed. Increasingly, areas are becoming available constrained by multiple boundary conditions from surface, airborne, and satellite surveys. This paper describes the implementation of continuation with multi-altitude boundary conditions in Cartesian and spherical coordinates and investigates the advantages and limitations of these applications. Continuations by EPS (Equivalent Point Source) inversion and the FT (Fourier Transform), as well as by SCHA (Spherical Cap Harmonic Analysis) are considered. These methods were selected because they are especially well suited for analyzing multi-altitude data over finite patches of the earth such as covered by the ADMAP database. In general, continuations constrained by multi-altitude data surfaces are invariably superior to those constrained by a single altitude data surface due to anomaly measurement errors and the non-uniqueness of continuation.

Kim, Jeong Woo↗
NASA NTRS2012

The Impact of Temporal Geopotential Variations on GPS

Lemoine et al. (2006) and Lemoine et al. (2010) showed that applying more detailed models of time-variable gravity (TVG) improved the quality of the altimeter satellite orbits (e.g. TOPEX/Poseidon, Jason-1, Jason-2). This modeling include application of atmospheric gravity derived from 6-hrly pressure fields obtained from the ECMWF and annual gravity variations to degree & order 20x20 in spherical harmonics derived from GRACE data. This approach allowed the development of a consistent geophysical model for application to altimeter satellite orbit determination from 1993 to 2011. In addition, we have also evaluated the impact of TVG modeling on the POD of Jason-1 and Jason-2 by application of a weekly degree & order four gravity coefficient time series developed using data from ten SLR & DORIS-tracked satellites from 1993 to 2011 (Lemoine et al., 2011).

Melachroinos, Stavros↗
NASA NTRS2013

The Effect of Seasonal and Long-Period Geopotential Variations on the GPS Orbits

We examine the impact of using seasonal and long-period time-variable gravity field (TVG) models on GPS orbit determination, through simulations from 1994 to 2012. The models of time-variable gravity that we test include the GRGS release RL02 GRACE-derived 10-day gravity field models up to degree and order 20 (grgs20x20), a 4 x 4 series of weekly coefficients using GGM03S as a base derived from SLR and DORIS tracking to 11 satellites (tvg4x4), and a harmonic fit to the above 4 x 4 SLR-DORIS time series (goco2s_fit2). These detailed models are compared to GPS orbit simulations using a reference model (stdtvg) based on the International Earth Rotation Service (IERS) and International GNSS Service (IGS) repro1 standards. We find that the new TVG modeling produces significant along, cross-track orbit differences as well as annual, semi-annual, draconitic and long-period effects in the Helmert translation parameters (Tx, Ty, Tz) of the GPS orbits with magnitudes of several mm. We show that the simplistic TVG modeling approach used by all of the IGS Analysis Centers, which is based on the models provided by the IERS standards, becomes progressively less adequate following 2006 when compared to the seasonal and long-period TVG models.

Orbit determination↗
NASA NTRS1994

Equatorial wave activity derived from fluctuations in observed convection

The spectrum of equatorial wave activity propagating vertically into the stratosphere is calculated from high-resolution imagery of the global convective pattern. Synoptic Global Cloud Imagery (GCI), constructed from six satellites simultaneously observing the earth, is used to diabatically force the linearized primitive equations. Having resolution of 0.5 deg and 3 h, that imagery captures the dominant scales of organized convection, including several harmonics of the diurnal cycle. Its global coverage with high space-time resolution allows the GCI to represent heating variability and dynamical behavior excited by it over a wide range of scales. The dynamical response above the heating is evaluated globally in terms of a space-time spectrum of Hough modes, one which includes planetary-scale Kelvin waves, Rossby waves, and gravity waves down to the resolution of the GCI. The geopotential response, which is indicative of temperature fluctuations observed by satellite, is very red in frequency. Therefore, planetary-scale waves with periods longer than two days dominate the spectrum of geopotential, while high-frequency gravity waves make a comparatively small contribution. Some 80% of the geopotential variance is accounted for by the Kelvin and gravest-symmetric Rossby modes, while the Rossby-gravity mode is comparatively weak. In horizontal eddy motion, the excited wave spectrum is still dominated by planetary-scale components. However, meridional wind fluctuations associated with the Rossby-gravity mode have variance comparable to that of zonal wind fluctuations associated with the Kelvin mode, even though the Rossby-gravity mode is nearly invisible in the geopotential response. Estimates of tropospheric heating lead to amplitudes and propagation characteristics that are broadly consistent with satellite and radiosonde observations of wave activity in the lower stratosphere. The space-time spectrum of EP flux is significantly whiter than the response in either geopotential or motion. Gravity waves of small scale and high frequency carry a large fraction of the upward flux. Although it dominates eastward variance of geopotential and motion, the Kelvin mode carries only about 50% of the eastward EP flux at phase speeds of 20-40 m/s and only 35% of the total eastward flux transmitted to the stratosphere. The remainder is carried by the gravity wave spectrum, which carries nearly all of the westward flux at phase speeds greater than 20 m/s. The gravity wave spectrum also contributes significantly at phase speeds of 10-20 m/s, where only 25% of the flux is accounted for by zonal wavenumbers less than 20. The broad nature of the gravity wave spectrum suggests its absorption at critical levels will be distributed over a deep layer of the middle atmosphere.

Bergman, John W.↗
NASA NTRS2007

Semianalytical Propagation of Satellite Orbits about an Arbitrary Central Body

Precision mean element (PME) satellite theories play a key role in orbit dynamics analyses. These theories employ: nonsingular orbital elements comprehensive force models Generalized Method of Averaging Numerical interpolation concepts The Draper Semianalytical Satellite Theory (DSST) (Refs. 1 - 6), whose development was led by the author, and the independently-developed Universal Semianalytical Method (USM) (Ref. 7) are examples of such theories. These theories provide the capability to tailor the force modeling to meet the desired computational speed vs. accuracy trade-off. The flexibility of such theories is demonstrated by their ability to include complicated atmosphere density models and spacecraft models in the perturbation theory context. The value of high speed satellite theories, in this era of computational plenty, is that they allow new ways of looking at astrodynamical problems such as orbit design (Refs. 8, 9) and atmosphere density updating (Refs. 10, 11). In the mid to late-1980 s, the geodynamics community led the development of very precise geopotential models such as GEM T2 and GEM T3 (Ref. 12), and with the subsequent analysis of the TOPEX flight data, JGM-2 and JGM-3 (Ref. 13). These were high degree and order geopotentials, at least 50 x 50. In 1993, the DSST implementation in the GTDS program was extended to include the 50 x 50 geopotential models (Ref. 14). The 50 x 50 geopotential, J2000 integration coordinate system, and solid Earth tide capabilities were integrated in GTDS by Scott Carter (Ref. 15). This capability demonstrated 1 m accuracy versus the TOPEX Precise Orbit Ephemerides. Subsequently the DSST Standalone program was also extended to include high degree and order geopotential models (Ref. 5). More recently GTDS has been hosted in the Linux PC environment. However, all of these efforts have been limited to modeling the motion of an artificial Earth satellite. They did not consider the additional complexities associated with lunar, planetary, or other natural satellite orbiters. Such complexities include: additional coordinate systems (associated with the direction of the north pole of rotation and the prime meridian of the new central bodies) (Ref. 16) normalized gravity model coefficients (desirable for high degree and order fields) (Ref. 17) indirect oblateness

Cefola, Paul J.↗
NASA NTRS1972

Error model for the SAO 1969 standard earth.

A method is developed for estimating an error model for geopotential coefficients using satellite tracking data. A single station's apparent timing error for each pass is attributed to geopotential errors. The root sum of the residuals for each station also depends on the geopotential errors, and these are used to select an error model. The model chosen is 1/4 of the difference between the SAO M1 and the APL 3.5 geopotential.

Martin, C. F.↗
NASA NTRS1984

Teleconnection patterns in the Southern Hemisphere

Contemporaneous correlations between geopotential heights on a given pressure surface at widely separated points on Earth, commonly referred to as teleconnections, are calculated from monthly mean sea level pressure and 500 mb geopotential height analyses for the Southern Hemisphere for five-month winter and summer seasons. During summer (November-March), anomalies over the three continents occur out of phase with anomalies over the subtropical oceans and in a wavenumber 3 pattern over the Southern Ocean near 55 deg S. The subtropical part of the pattern appears largely associated with the interannual variation of the seasonal cycle and annual mean. In winter (May-September) 500 mb geopotential heights over Africa exhibit positive correlations with heights over South America and the central South Pacific near New Zealand and negative correlations with height over the Southern Ocean. A striking wavenumber three pattern is apparent which shows the correlation of 500 mb geopotential height anomalies with 500 mb anomalies at 50 deg S, 95 deg E during winter. The strong positive correlations between 50 deg S, 95 E and 58 deg S, 150 deg W and 38 deg S, 15 deg W contrast with negative correlations over Antarctica and in low latitudes. Time variations in a similar pattern in sea level pressure are in phase with variations in the 500 mb pattern, suggesting an equivalent barotropic structure.

Mo, K. C.↗
NASA NTRS1985

Middle Atmosphere Reference Model Derived from Satellite Data

Zonally averaged temperature and geostrophic zonal wind for each month and for latitudes from 80 S to 80 N with pressure scale height as a vertical coordinate are given tabular form. The pressure scale height is defined as -ln (p/P sub O) where p is pressure and P sub O is surface pressure. The height interval corresponding to one pressure scale height is proportional to absolute temperature, and is 7 km at 240 K. Values in are given at intervals of 0.5 pressure scale heights, i.e., approximately 3,5 km. The geopotential height fields for the principal seasons are given. Temperature, pressure and density with geometric height as the vertical coordinate at invervals of 5 km. The temperature values were obtained from a combination of satellite data above 30 mb with values supplied by the Berlin Free University at 30 mb and the climatology derived by OORT (1983) for 50 mb and below. The geopotential height fields were obtained from these temperature fields by integrating up and down from the 30 mb geopotential height supplied by Berlin Free University. The geostrophic winds were obtained by differentiating these geopotential height fields.

Barnett, J. J.↗
NASA NTRS1992

An assessment of gravity model improvements using TOPEX/Poseidon TDRSS observations

The contribution of TOPEX/Poseidon (T/P) TDRSS data to geopotential model recovery is assessed. Simulated TDRSS one-way and Bilateration Ranging Transponder System (BRTS) observations have been generated and orbitally reduced to form normal equations for geopotential parameters. These normals have been combined with those of the latest prelaunch T/P gravity model solution using data from over 30 satellites. A study of the resulting solution error covariance shows that TDRSS can make important contributions to geopotential recovery, especially for improving T/P specific effects like those arising from orbital resonance. It is argued that future effort is desirable both to establish TDRSS orbit determination limits in a reference frame compatible with that used for the precise laser/DORIS orbits, and the reduction of these TDRSS data for geopotential recovery.

Putney, B. H.↗
NASA NTRS2003

An Evaluation of Recent Gravity Models wrt. Altimeter Satellite Missions

With the launch of CHAMP and GRACE, we have entered a new phase in the history of satellite geodesy. For the first time, geopotential models are now available based almost exclusively on satellite-satellite tracking either with GPS in the case of the CHAMP-based geopotential models, or co-orbital intersatellite ultra-precise ranging in the case of GRACE. Different groups have analyzed these data, and produced a series of geopotential models (e.g., EIGENlS, EIGEN2, GGM0lS, GGMOlC) that incorporate the new data. We will compare the performance of these "newer" geopotential models with the standard models now used for computations, (e.g., JGM-3, BGM-96, PGS7727, and GRIMS-C1) for TOPEX, JASON, Geosat-Follow-On (GFO), and Envisat using standard metrics such as SLR RMS of fit, altimeter crossovers, and orbit overlaps. Where covariances are available we can evaluate the predicted geographically correlated orbit error. These predicted results can be compared with the Earth-fixed differences between dynamic and reduced-dynamic orbits to test the predictive accuracy of the covariances, as well as to calibrate the error of the solutions.

Lemoine, Frank G.↗
NASA NTRS1972

Atmospheric wind fields derived from Nimbus ozone measurements

The global ozone measurements made by the Nimbus 3 IRIS were used to trace the circulation in the upper troposphere. This was possible because the atmospheric ozone content is closely related to the geopotential heights in the upper troposphere. There is a linear relationship between 200 mbar geopotential heights and the total ozone measured by Nimbus 3. With the help of the geostrophic law, atmospheric winds can be derived from the horizontal gradient of the geopotential heights. Utilizing the linear relationship shown, winds can be deduced from satellite measurements of total ozone.

Prabhakara, C.↗
NASA NTRS1975

On the tesseral-harmonics resonance problem in artificial-satellite theory

The longitude-dependent part of the geopotential usually gives rise only to short-period effects in the motion of an artificial satellite. However, when the motion of the satellite is commensurable with that of the earth, the path of the satellite repeats itself relative to the earth and perturbations build up at each passage of the satellite in the same spot, so that there can be important long-period effects. In order to take these effects into account in deriving a theoretical solution to the equations of motion of an artificial satellite, it is necessary to select terms in the longitude-dependent part of the geopotential that will contribute significantly to the perturbations. Attempts made to obtain a selection that is valid in a general case, regardless of the initial eccentricity of the orbit and of the order of the resonance, are reported. The solution to the equations of motion of an artificial satellite, in a geopotential thus determined, is then derived by using Hori's method by Lie series, which, by its properties regarding canonical invariance, has proved advantageous in the classical theory.

Romanowicz, B. A.↗
NASA NTRS1975

Fourteen years of resonance of Vanguard orbits

Tracking of Vanguard 3 and the Vanguard 2 rocket with Baker-Nunn cameras and the U.S. Navy's Space Surveillance (radio interferometer) system over a 14 year period revealed resonant fluctuations of up to 0.035 deg in inclination (peak to peak). Six geopotential terms (lumped coefficients) of 11th order and three of 22nd order were measured using orbit inclinations derived from this tracking record. The terms of 11th order are significantly smaller than Kaula's rule. (The lumped coefficients are sensitive to geopotential effects as high as 37th degree.) These observed terms are compatible with a recent 27-satellite geopotential solution whose formal coefficient errors are increased by a factor of 3.3.

Wagner, C. A.↗
NASA NTRS1975

Sequential filtering applied to the determination of tracking station locations

The extended sequential filter has been applied to the problem of dynamically determining the geocentric coordinates of two laser satellite tracking stations. This filter provides significant advantages over the classical batch methods through (1) fewer iterations required for convergence, (2) wider radius of convergence, and (3) availability of the parameter estimate evolution. Processing the data sequentially readily identifies the data arcs required to minimize the effects of geopotential model errors. By means of the Smithsonian standard earth 2 and the Goddard earth model 1 geopotentials to reduce laser range observations of the Beacon Explorer-C satellite, it is demonstrated that a two-pass arc is optimal for estimating the height of one station and all coordinates of the second station while minimizing the effect of geopotential model error. These two-pass estimates are in good agreement with other determinations that utilize considerably more data as well as different satellites.

Schutz, B. E.↗
NASA NTRS1975

The exterior tidal potential acting on a satellite

A theory is presented that points out the existence of several long period and 'cross effects' in the coefficients in the expansion of the geopotential and in the motion of satellites. The tidal potential, defined as small periodic variations in the geopotential, was calculated. The influence of these geopotential variations on satellite perturbation is examined. Spherical harmonics were employed.

Musen, P.↗