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At least 163 records · Page 9

The theory of the gravitational potential applied to orbit prediction

A complete derivation of the geopotential function and its gradient is presented. Also included is the transformation of Laplace's equation from Cartesian to spherical coordinates. The analytic solution to Laplace's equation is obtained from the transformed version, in the classical manner of separating the variables. A cursory introduction to the method devised by Pines, using direction cosines to express the orientation of a point in space, is presented together with sample computer program listings for computing the geopotential function and the components of its gradient. The use of the geopotential function is illustrated.

Kirkpatrick, J. C.↗

Radial orbit error reduction and sea surface topography determination using satellite altimetry

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface topography with minimum wavelengths of about 500 km and to reduce the radial orbit error caused by geopotential errors. The modeling of the radial orbit error is made using the linearized Lagrangian perturbation theory. Secular and second order effects are also included. After a rather extensive validation of the linearized equations, alternative expressions of the radial orbit error are derived. Numerical estimates for the radial orbit error and geoid undulation error are computed using the differences of two geopotential models as potential coefficient errors, for a SEASAT orbit. To provide statistical estimates of the radial distances and the geoid, a covariance propagation is made based on the full geopotential covariance. Accuracy estimates for the SEASAT orbits are given which agree quite well with already published results. Observation equations are develped using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information provides estimates of parameters representing the sea surface topography and corrections to the gravity field that is used for the orbit generation. The simulation results show that the method can be used to effectively reduce the radial orbit error and recover the sea surface topography.

Engelis, Theodossios↗

Assimilation of scalar versus horizontal gradient information from the VAS into a mesoscale model

Comparisons are made between analyses and forecasts which incorporate VAS geopotential data as either scalar or horizontal gradient information for a case study on the AVE/VAS day of Mar. 6, 1982. On this day, incorporating the VAS information in analysis as a variational constraint on horizontal geopotential gradients significantly mitigated the effects of large data biases which made VAS assimilation by standard scalar methods very difficult. A subsequent forecast made from the gradient assimilation was superior to one made from the standard analysis and of comparable quality in geopotentials to a control forecast from synoptic data. Most impact was noted in the forecasts of vertical motion and precipitation in the gradient vs this control simulation.

Diak, George↗

Global atmospheric circulation statistics: Four year averages

Four year averages of the monthly mean global structure of the general circulation of the atmosphere are presented in the form of latitude-altitude, time-altitude, and time-latitude cross sections. The numerical values are given in tables. Basic parameters utilized include daily global maps of temperature and geopotential height for 18 pressure levels between 1000 and 0.4 mb for the period December 1, 1978 through November 30, 1982 supplied by NOAA/NMC. Geopotential heights and geostrophic winds are constructed using hydrostatic and geostrophic formulae. Meridional and vertical velocities are calculated using thermodynamic and continuity equations. Fields presented in this report are zonally averaged temperature, zonal, meridional, and vertical winds, and amplitude of the planetary waves in geopotential height with zonal wave numbers 1-3. The northward fluxes of sensible heat and eastward momentum by the standing and transient eddies along with their wavenumber decomposition and Eliassen-Palm flux propagation vectors and divergences by the standing and transient eddies along with their wavenumber decomposition are also given. Large interhemispheric differences and year-to-year variations are found to originate in the changes in the planetary wave activity.

Wu, M. F.↗

Relative motion using analytical differential gravity

This paper presents a new approach to the computation of the motion of one satellite relative to another. The trajectory of the reference satellite is computed accurately subject to geopotential perturbations. This precise trajectory is used as a reference in computing the position of a nearby body, or bodies. The problem that arises in this approach is differencing nearly equal terms in the geopotential model, especially as the separation of the reference and nearby bodies approaches zero. By developing closed form expressions for differences in higher order and degree geopotential terms, the numerical problem inherent in the differencing approach is eliminated.

Gottlieb, Robert G.↗

Global atmospheric circulation statistics, 1000-1 mb

The atlas presents atmospheric general circulation statistics derived from twelve years (1979-90) of daily National Meteorological Center (NMC) operational geopotential height analyses; it is an update of a prior atlas using data over 1979-1986. These global analyses are available on pressure levels covering 1000-1 mb (approximately 0-50 km). The geopotential grids are a combined product of the Climate Analysis Center (which produces analyses over 70-1 mb) and operational NMC analyses (over 1000-100 mb). Balance horizontal winds and hydrostatic temperatures are derived from the geopotential fields.

Randel, William J.↗

Investigation of a geodesy coexperiment to the Gravity Probe B relativity gyroscope program

Geodesy is the science of measuring the gravitational field of and positions on the Earth. Estimation of the gravitational field via gravitation gradiometry, the measurement of variations in the direction and magnitude of gravitation with respect to position, is this dissertation's focus. Gravity Probe B (GP-B) is a Stanford satellite experiment in gravitational physics. GP-B will measure the precession the rotating Earth causes on the space time around it by observing the precessions of four gyroscopes in a circular, polar, drag-free orbit at 650 km altitude. The gyroscopes are nearly perfect niobium-coated spheres of quartz, operating at 1.8 K to permit observations with extremely low thermal noise. The permissible gyroscope drift rate is miniscule, so the torques on the gyros must be tiny. A drag-free control system, by canceling accelerations caused by nongravitational forces, minimizes the support forces and hence torques. The GP-B system offers two main possibilities for geodesy. One is as a drag-free satellite to be used in trajectory-based estimates of the Earth's gravity field. We described calculations involving that approach in our previous reports, including comparison of laser only, GPS only, and combined tracking and a preliminary estimate of the possibility of estimating relativistic effects on the orbit. The second possibility is gradiometry. This technique has received a more cursory examination in previous reports, so we concentrate on it here. We explore the feasibility of using the residual suspension forces centering the GP-B gyros as gradiometer signals for geodesy. The objective of this work is a statistical prediction of the formal uncertainty in an estimate of the Earth's gravitation field using data from GP-B. We perform an instrument analysis and apply two mathematical techniques to predict uncertainty. One is an analytical approach using a flat-Earth approximation to predict geopotential information quality as a function of spatial wavelength. The second estimates the covariance matrix arising in a least-squares estimate of a spherical harmonic representation of the geopotential using GP-B gradiometer data. The results show that the GP-B data set can be used to create a consistent estimate of the geopotential up to spherical harmonic degree and order 60. The formal uncertainty of all coefficients between degrees 5 and 50 is reduced by factors of up to 30 over current satellite-only estimates and up to 7 over estimates which include surface data. The primary conclusion resulting from this study is that the gravitation gradiometer geodesy coexperiment to GP-B is both feasible and attractive.

Everitt, C. W. F.↗

On ozone correlation with meteofields in the Northern Hemisphere

The correlation coefficients of temperature and geopotential heights at various levels with total ozone and its vertical distribution have been analyzed, using the ground based and ozone sounding data. Two independent groups of factors affect total ozone. The first group - the geopotential values of the troposphere - stratosphere border (100-500 mb) manifest themselves most of all in the middle latitudes. Pertaining to this group is the total ozone correlation with the tropopause height and temperature at 500 mb. The correlation coefficients are negative (-0.55 -0.65) and little depend on the season. Related to this factor is a high (up to 0.8) correlation of ozone partial pressure with the temperature in the lower stratosphere. The second group is the geopotential and temperature values at the 10-30 mb coefficients (up to 0.6) are observed in winter in the subpolar latitudes. In summer they are substantially lower - about 0.1.

Kadygrova, Tatiana V.↗

The 4-Day Wave as Observed from the Upper Atmosphere Research Satellite Microwave Limb Sounder

The "4-day wave" is an eastward moving quasi-nondispersive feature with period near 4 days occurring near the winter polar stratopause. This paper presents evidence of the 4-day feature in Microwave Limb Sounder (MLS) temperature, geopotential height, and ozone data from the late southern winters of 1992 and 1993. Space-time spectral analyses reveal a double-peaked temperature structure consisting of one peak near the stratopause and another in the lower mesosphere, with an out-of-phase relationship between the two peaks. This double- peaked structure is reminiscent of recent three-dimensional barotropic/baroclinic instability model predictions and is observed here for the first time. The height variation of the 4-day ozone signal is shown to compare well with a linear advective-photochemical tracer model. Negative regions of quasigeostrophic potential vorticity (PV) gradient and positive Eliassen-Palm flux divergence are shown to occur, consistent with instability dynamics playing a role in wave forcing. Spectral analyses of PV derived from MLS geopotential height fields reveal a 4-day signal peaking near the polar stratopause. The three-dimensional structure of the 4-day wave resembles the potential vorticity "charge" concept, wherein a PV anomaly in the atmosphere (analogous to an electrical charge in a dielectric material) induces a geopotential field, a vertically oriented temperature dipole, and circulation about the vertical axis.

Allen, D. R.↗

An Assessment of Gravity Recovery with CHAMP Data

The CHAMP mission, launched in July 2000, is the first in the series of mapping missions for the Earth's geopotential scheduled for the first decade of the new millenium. Its unique contributions compared to all the previous generation of satellites whose data have been included in Earth geopotential models are the precision global tracking with GPS data, and the availability of precision accelerometry data to model the nonconservative forces. Over the past year we have implemented extensive modifications to our GEODYN orbit determination processing code and ancillary data preprocessors to process the GPS and accelerometry data from missions such as CHAMP and GRACE. We report on the analysis of up to 60 days of CHAMP data and how these data contribute to Earth geopotential solutions where the base model is a derivative of EGM96. Preliminary results with only 12.5 days of data processed clearly show the ability of the CHAMP data to improve the modeling of the zonals (1=10 to 40), the m-dailies, the primary resonance terms, and the sectoral harmonics. We will detail the results of our calibrations of the CHAMP accelerometry and assess the quality of test solutions that include these CHAMP data.

Lemoine, F. G.↗

Gravity Fields from CHAMP Mission Data

The CHAMP mission, launched in July 2000, is the first in a series of missions that will revolutionize our ability to model the Earth s geopotential. The CHAMP spacecraft is equipped for precision tracking by the Global Positioning System (GPS) and Satellite Laser Ranging (SLR) along with a precision accelerometer to provide measurements of the surface forces. Preliminary satellite-only geopotential solutions with only 30 days of CHAMP data are, by some criteria, as strong as solutions made from tracking data collected over the previous 30 years of the space age. Compared to EGM96, CHAMP makes notable contributions in regions where the terrestrial data (surface gravimetry and altimetry) were weak, for example in the polar regions, in the Amazon and the Himalayas. The CHAMP data allow us to separate the geoid from the dynamic ocean topography (DOT) up to at least degree 25 rather than just under degree 20 as in EGM96. We report on satellite-only and combination models that incorporate up to 100 days of CHAMP data as well as other satellite data. We report on our updated processing of the CHAMP tracking and accelerometer data and evaluate the performance of the geopotential models using a variety of tests.

Lemoine, Frank G.↗

Remote Influence of Andean Convection on Amazonian Rainfall and Its Mechanisms

Models from Coupled Model Intercomparison Project Phase 6 produce too much precipitation over the Andes but too little over the Amazon or the Wet Andes-Dry Amazon (WADA) bias pattern. Unlike the conventional view that convection parameterization and land model deficiencies can contribute to Amazonian rainfall biases, we approach this long-standing biased model behavior through the lens of Andean convection. Using Community Earth System Model v1.1 and focusing on the wet season, our mechanism-denial experiments demonstrate that Andean convection notably reduces precipitation over the Amazon during austral summer. The Andean forced Amazonian response operates on weather timescale. Furthermore, the reduction of Amazonian rainfall is detectable within a few hours after initial Andean forcing. The precipitation response is primarily driven by variations in the moisture budget and is moderated by changes in convective available potential energy over the Amazon. Changes in the total advection of moisture over the Amazon are dominated by the vertical advection term and can be attributed to discrepancies in the dynamic omega field. In the experiments, the Andean east flank region is scrutinized where the vertical velocity and moisture fields play an intermediary role for the Andean driven WADA connection. The Andean forcing induces descending anomalies on the Andean east flank. The disturbances of wind and geopotential fields over the Andean east flank propagate eastward via Kelvin waves. Over the Amazon, descending anomalies and advective drying lead to reduction of mid-to-high level cloud, increase of shortwave cloud forcing and surface net radiation, and enhancement of themodynamic stability and rainfall reduction.

58 GEOSCIENCES↗

Topological Signature of Stratospheric Poincaré-Gravity Waves

The rotation of Earth breaks time-reversal and reflection symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator, the rotating shallow-water and stably stratified primitive equations exhibit Poincaré inertia–gravity waves that have nontrivial topology as evidenced by their strict superinertial time scale and a phase singularity in frequency–wavevector space. This nontrivial topology then predicts, via the principle of bulk-interface correspondence, the existence of two equatorial waves along the equatorial interface, the Kelvin and Yanai waves. To directly test the nontrivial topology of Poincaré-gravity waves in observations, we examine ERA5 data and study cross correlations between the wind velocity and geopotential height of the midlatitude stratosphere at the 50 hPa height. We find the predicted vortex and antivortex in the relative phase of the geopotential height and velocity at the high frequencies of the waves. By contrast, lower-frequency planetary waves are found to have trivial topology also as expected from theory. These results demonstrate a new way to understand stratospheric waves and provide a new qualitative tool to investigate waves in other components of the climate system.

54 ENVIRONMENTAL SCIENCES↗

Lidar-Based Evaluation of HRRR Performance in California’s Diablo Range

The performance of the NOAA High-Resolution Rapid Refresh (HRRR) model for capturing low-level winds near a wind energy production site during summer 2019 is evaluated. This study catalogs the ability of HRRR to predict boundary layer dynamics relevant to wind energy interests over complex terrain, which has presented challenges for weather and energy forecasting. Performance is evaluated by comparing HRRR output to wind-profiling Doppler lidars at Lawrence Livermore National Laboratory Site 300. HRRR captured the diurnal profile of horizontal winds in the observed 150-m layer, despite strong underpredictions (∼4 m s −1 ) during evening and nighttime hours. These underpredictions may be a result of local speedup flows observed by the lidars, which were unresolved in HRRR due to their small spatial extent. HRRR bias magnitude relative to observations was found to be minimal during days with synoptic-scale troughs and strong 850-hPa geopotential gradients, while bias magnitude was maximal during days with synoptic ridging and weak 850-hPa geopotential gradients. To translate wind speed predictions to energy forecasting, generic turbine models were used to estimate power generation for turbines characteristic of the nearby Altamont Pass Wind Resource Area. Results show that HRRR-based energy estimates predicted daytime power generation adequately relative to lidar-based estimates with an 18-h lead time (bias magnitude < 0.4 MW from 0900 to 1400 LT) but overpredicted power during the rest of the diurnal cycle (bias > 1 MW). These results demonstrate conditions under which HRRR performs well for wind energy applications in complex terrain, while highlighting biases that require further investigation to support usage of a high-resolution model for wind energy forecasts.

Boundary layer↗

Global distribution of total ozone derived from Nimbus 3 satellite during April July, 1969 and its implication to upper tropospheric circulation

Utilizing a stepwise multiple regression scheme, monthly mean global maps of total ozone are produced from the spectral intensity measurements made by the infrared interferometer spectrometer (IRIS) onboard the Nimbus 3 satellite for the period April 18 to July 22, 1969. These maps show that over the equatorial regions total ozone increases steadily from April to July. Further, latitudinal variation of total ozone derived from these maps shows that the ozone increases at all latitudes over the Southern Hemisphere uniformly from April to July while over the Northern Hemisphere the monthly decrease at all latitudes is nonuniform. In general, these maps bear a close resemblance to the upper tropospheric circulation. It is observed that the total ozone is best correlated with the 200 mb geopotential heights. This relationship enables the utilization of total ozone as a quasi-stream function to determine geostrophic winds at 200 mb level. Further, even at low latitudes where the total ozone does not bear simple relationship to the geopotential heights the course of the easterly jet stream with the help of the ozone measurements can be identified.

Prabhakara, C.↗

Gravitational field models for the earth (GEM 1 and 2)

Two models of the earth's gravitational field have been computed at Goddard Space Flight Center. The first, Goddard Earth Model 1 (GEM 1), has been derived from satellite tracking data. The second, Goddard Earth Model 2 (GEM 2), has been derived from a combination of satellite tracking and surface gravimetric data. The geopotential models are represented in spherical harmonics complete to degree and order 16 for the combined solution and complete to degree and order 12 for the satellite solution. Both solutions include zonal terms to degree 21 and related satellite resonant coefficients to degree 22. The satellite data consisted primarily of optical data processed on 300 weekly orbital arcs for 25 close earth satellites. Surface gravity data were employed in the form of 5 deg x 5 deg mean free-air gravity anomalies providing about 70% world coverage. Station locations were obtained for 46 tracking sites by combining electronic, laser, and additional optical tracking data with the above satellite data. Analysis of the radial positions of these stations and a value of mean gravity on the geoid indicated a mean equatorial radius for the earth of about 6378145 meters. Results of geopotential tests on satellite data not used in the solution show that better agreement was obtained with the GEM 1 and GEM 2 models than with the 1969 Smithsonian Standard Earth 2 model.

Lerch, F. J.↗

Determination of the geoid from satellite altimeter data

The characteristics of the geoid surface are quantitatively described. A procedure for calculating the satellite altitude is developed. Error sources are described quantitatively, mathematically modeled, and evaluated in computer simulation. Procedures for maximum likelihood processing of altimeter data for recovery of orbit and geopotential information are presented for several geopotential models.

Brown, R. D.↗

Tests and comparisons of gravity models.

Optical observations of the GEOS satellites were used to obtain orbital solutions with different sets of geopotential coefficients. The solutions were compared before and after modification to high order terms (necessary because of resonance) and were then analyzed by comparing subsequent observations with predicted trajectories. The most important source of error in orbit determination and prediction for the GEOS satellites is the effect of resonance found in most published sets of geopotential coefficients. Modifications to the sets yield greatly improved orbits in most cases. The results of these comparisons suggest that with the best optical tracking systems and gravity models, satellite position error due to gravity model uncertainty can reach 50-100 m during a heavily observed 5-6 day orbital arc. If resonant coefficients are estimated, the uncertainty is reduced considerably.

Marsh, J. G.↗