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NASA NTRS1984

Solar Inverse Theory

Helioseismological inversion, as with the inversion of any other data, is divided into three phases. The first is the solution of the so-called forward problem: namely, the calculation of the eigenfrequencies of a theoretical equilibrium state. The second is an attempt to understand the results, either empirically by determining how those frequencies vary as chosen parameters defining the equilibrium model are varied, or analytically from asymptotic expansions in limiting cases of high order or degree. The third phase is to pose and solve an inverse problem, which seeks to find a plausible equilibrium model of the Sun whose eigenfrequencies are consistent with observation. The three phases are briefly discussed in this review, and the third, which is not yet widely used in helioseismology, is illustrated with some selected inversions of artificial solar data.

Gough, D.↗
NASA NTRS1974

Analysis of RAE-1 inversion

The RAE-1 spacecraft inversion performed October 31, 1972 is described based upon the in-orbit dynamical data in conjunction with results obtained from previously developed computer simulation models. The computer simulations used are predictive of the satellite dynamics, including boom flexing, and are applicable during boom deployment and retraction, inter-phase coast periods, and post-deployment operations. Attitude data, as well as boom tip data, were analyzed in order to obtain a detailed description of the dynamical behavior of the spacecraft during and after the inversion. Runs were made using the computer model and the results were analyzed and compared with the real time data. Close agreement between the actual recorded spacecraft attitude and the computer simulation results was obtained.

Hedland, D. A.↗
NASA NTRS2007

Evaluating the Capacity of Global CO2 Flux and Atmospheric Transport Models to Incorporate New Satellite Observations

As we enter the new era of satellite remote sensing for CO2 and other carbon cyclerelated quantities, advanced modeling and analysis capabilities are required to fully capitalize on the new observations. Model estimates of CO2 surface flux and atmospheric transport are required for initial constraints on inverse analyses, to connect atmospheric observations to the location of surface sources and sinks, and ultimately for future projections of carbon-climate interactions. For application to current, planned, and future remotely sensed CO2 data, it is desirable that these models are accurate and unbiased at time scales from less than daily to multi-annual and at spatial scales from several kilometers or finer to global. Here we focus on simulated CO2 fluxes from terrestrial vegetation and atmospheric transport mutually constrained by analyzed meteorological fields from the Goddard Modeling and Assimilation Office for the period 1998 through 2006. Use of assimilated meteorological data enables direct model comparison to observations across a wide range of scales of variability. The biospheric fluxes are produced by the CASA model at lxi degrees on a monthly mean basis, modulated hourly with analyzed temperature and sunlight. Both physiological and biomass burning fluxes are derived using satellite observations of vegetation, burned area (as in GFED-2), and analyzed meteorology. For the purposes of comparison to CO2 data, fossil fuel and ocean fluxes are also included in the transport simulations. In this presentation we evaluate the model's ability to simulate CO2 flux and mixing ratio variability in comparison to in situ observations at sites in Northern mid latitudes and the continental tropics. The influence of key process representations is inferred. We find that the model can resolve much of the hourly to synoptic variability in the observations, although there are limits imposed by vertical resolution of boundary layer processes. The seasonal cycle and its interannual variations generally respond adequately, but discrepancies in the tropics suggest the need for a refinement of the soil moisture dependence of the respiration flux in CASA. Examples and inferences for interpretation of satellite data will be discussed. In general, the fidelity of these simulations leads us to anticipate incorporation of real-time, highly resolved remote sensing and other observations into quantitative analyses that will reduce uncertainty in the terrestrial CO2 sink and revolutionize our understanding of the key processes controlling atmospheric CO2 and its evolution with time.

Kawa, S. R.↗
NASA NTRS1991

Remote sensing of earth terrain

In remote sensing, the encountered geophysical media such as agricultural canopy, forest, snow, or ice are inhomogeneous and contain scatters in a random manner. Furthermore, weather conditions such as fog, mist, or snow cover can intervene the electromagnetic observation of the remotely sensed media. In the modelling of such media accounting for the weather effects, a multi-layer random medium model has been developed. The scattering effects of the random media are described by three-dimensional correlation functions with variances and correlation lengths corresponding to the fluctuation strengths and the physical geometry of the inhomogeneities, respectively. With proper consideration of the dyadic Green's function and its singularities, the strong fluctuation theory is used to calculate the effective permittivities which account for the modification of the wave speed and attenuation in the presence of the scatters. The distorted Born approximation is then applied to obtain the correlations of the scattered fields. From the correlation of the scattered field, calculated is the complete set of scattering coefficients for polarimetric radar observation or brightness temperature in passive radiometer applications. In the remote sensing of terrestrial ecosystems, the development of microwave remote sensing technology and the potential of SAR to measure vegetation structure and biomass have increased effort to conduct experimental and theoretical researches on the interactions between microwave and vegetation canopies. The overall objective is to develop inversion algorithms to retrieve biophysical parameters from radar data. In this perspective, theoretical models and experimental data are methodically interconnected in the following manner: Due to the complexity of the interactions involved, all theoretical models have limited domains of validity; the proposed solution is to use theoretical models, which is validated by experiments, to establish the region in which the radar response is most sensitive to the parameters of interest; theoretically simulated data will be used to generate simple invertible models over the region. For applications to the remote sensing of sea ice, the developed theoretical models need to be tested with experimental measurements. With measured ground truth such as ice thickness, temperature, salinity, and structure, input parameters to the theoretical models can be obtained to calculate the polarimetric scattering coefficients for radars or brightness temperature for radiometers and then compare theoretical results with experimental data. Validated models will play an important role in the interpretation and classification of ice in monitoring global ice cover from space borne remote sensors in the future. We present an inversion algorithm based on a recently developed inversion method referred to as the Renormalized Source-Type Integral Equation approach. The objective of this method is to overcome some of the limitations and difficulties of the iterative Born technique. It recasts the inversion, which is nonlinear in nature, in terms of the solution of a set of linear equations; however, the final inversion equation is still nonlinear. The derived inversion equation is an exact equation which sums up the iterative Neuman (or Born) series in a closed form and, thus, is a valid representation even in the case when the Born series diverges; hence, the name Renormalized Source-Type Integral Equation Approach.

Yueh, Herng-Aung↗
NASA NTRS2018

Estimation of Lower-Body Kinetics from Loading Profile and Kinematics Alone, Without Measured Ground Reaction Forces

Biomechanical models of human motion can estimate kinetic outcomes, such as joint moments, joint forces and muscle forces. Typically, one performs an inverse dynamics (ID) analysis to compute joint moments from joint angles and measured external forces. Sometimes it is impractical to measure ground reaction forces and moments (GRF&M). We devised an empirical method for performing ID analysis of resistance exercises without measured GRF&M. The method solves the multibody dynamics equations of motion with four key assumptions about the GRF&M that reduce the number of unknowns. The assumptions are 1) negligible ground reaction moments, 2) fixed lateral/medial location of the center of pressure (COP), 3) equal fore/aft location of the COP between the feet, and 4) constant angle of the GRF vector relative to the vertical axis in the frontal plane. We used evaluation trials from a spaceflight countermeasure resistance training device to test this approach. Four participants performed squat and deadlift exercises at various loads. We compared results from traditional ID analysis to results without measured GRF&M using our method. We found that joint moment trajectories in the sagittal plane were qualitatively similar in shape between the two methods, and the amount of root mean squared error (RMSE), measured by difference in joint moment impulse, was typically under 10 percent. Non-sagittal joint moment trajectories, which are much lower in overall magnitude, were not qualitatively similar in shape between the two methods. Non-sagittal moments displayed much higher RMSE, with typical values well over 50 percent. These findings were further supported by validation metrics (Sprague and Geers' P and M metrics, Pearson's r correlation coefficient). Based on these findings, we concluded that useful kinetic results are obtained from ID analysis of squat and deadlift exercises, even when GRF&M are not measured, as long as the outcomes of interest lie in the sagittal plane.

computational modeling↗
NASA NTRS1980

A fast and accurate radiance algorithm for application to inversion of limb measurements

A method is devised to accurately calculate broad band limb radiance based on a precalculated data base consisting of homogeneous path emissivity as a function of mass path data for various temperatures and pressures. Accurately estimating limb radiance by splicing together interpolated information from the emissivity curves requires no temperature or pressure weighting, and only two interpolations per layer path. The emissivity growth approximation (EGA) technique is applied in a simulated inversion study to the inference of O3, H2O, NO2 and HNO3, and it is found to have comparable accuracies to more sophisticated many-degree band models. The EGA technique is also found to be two orders of magnitude faster, while requiring one second per inversion for one constituent at one-km resolution, allowing a completely nonlinear relaxation time inversion to be done at linear speeds. The technique is also expected to work well for nadir calculations, and prove adequate for estimating occultation radiances.

Gordley, L. L.↗
NASA NTRS1999

Inversion of Gravity Fields From the Spacecraft Orbital Data Using an Adjoint Operator Approach

In perturbation approximation, the forward problem of orbital dynamics (equations with initial conditions) is linear with respect to variations of coordinates and/or velocities of the spacecraft and to corresponding variations of the gravity field in the models used. The linear operator adjoint to the linear operator of such forward problem turns out to be instrumental in inversion of differences between observed and predicted coordinates/velocities in terms of the updates of harmonics in the initial gravity field model. Based on this approach, the solution of resulting adjoint problem of orbital dynamics can be used to directly evaluate the matrix of partial derivatives of observable differences with respect to the gravity field harmonics. General discussion of the adjoint problem of orbital dynamics is given and an example of a mathematical formalism for the practical retrieval algorithm is presented.

Ustinov, E. A.↗
NASA NTRS1974

Inviscid to turbulent transition of trailing vortices

The characteristics of the plateau region in the vortex system which trails from a lifting wing are discussed. The decay of the vortex due to viscous or turbulent shear is very slow in the plateau so that the maximum tangential speed in the vortices remains nearly constant for some distance downstream of roll-up and then begins to decrease, becoming inversely proportional to the square root of the distance downstream. Mathematical models are developed to analyze the structure of the plateau area. Solutions are obtained for both constant and variable eddy viscosity models.

Iversen, J. D.↗
NASA NTRS1975

Venus - Vertical structure of stratospheric hazes from Mariner 10 pictures

An 'optical barometer' technique for determining the altitudes of haze in the stratosphere of Venus is presented wherein the Rayleigh-scattering component is derived by comparing orange and UV brightness profiles for nearby Mariner 10 television-picture pairs. The derived scale height for CO2 gas is 4.2 km, corresponding to a temperature of 200 K, in good agreement with radio occultation data. The optical barometer yields a pressure of 4 mb for the level at which the slant-path optical depth at the limb is unity. This level corresponds to a distance from the center of Venus equal to 6131 km, which is accurate to within 1 km provided that there is no appreciable contribution to the brightness by Rayleigh-scattering aerosols which mimic CO2 gas. It is possible that the limb haze layering observed between 6130 and 6140 km could be correlated with temperature inversions detected by the Mariner 5 radio-occultation experiment. A model is proposed wherein the concentration of particles increases rapidly with an effective scale height of about 2 km as one descends about 10 km from the limb haze to the main polarization cloud deck.

Oleary, B.↗
NASA NTRS1978

Further studies of trace elements in C3 chondrites

Five carbonaceous chondrites (Renazzo C2V, Allende C3V, Ornans C3O, Warrenton C3O, and Orgueil C1) were analyzed by radiochemical neutron activation analysis for 20 elements. Elements condensing between approximately 700 and 420 K are systematically more depleted than those condensing between 1000 and 900 K, and the depletion correlates inversely with matrix content and directly with degree of metamorphism. A model of gas-dust fractionation during condensation, by settling of dust to the median plane of the nebula, is proposed. Gas/dust ratios relative to the cosmic ratio ranged from 0.7 at 1000 K to 0.5 at 700 K for C3O chondrites that accreted first and from 1.3 to 0.6 for the last. No further gas/dust fractionation was indicated below 700 K

Takahashi, H.↗
NASA NTRS1978

SS Cygni as a hard X-ray source identified with the scanning modulation collimator on HEAO 1

Hard X-ray emission from a 15 min by 1.5 deg area containing SS Cygni had previously been reported and identified with SS Cygni. This paper reports a 0.4 sq arc min measurement of the position of the X-ray source with the HEAO 1 modulation collimator experiment which leads to an unequivocal identification of SS Cygni as an X-ray emitter in the 2-10 keV energy range. The historical light curve in hard X-rays was also investigated by analyzing relevant Uhuru data, and two instances of possible source detection in the 2-6 keV band were noted. From Ariel 5 observations it is calculated that the X-ray luminosity of SS Cygni in the 2-10 keV energy range is of the order of 10 to the 33rd erg/sec in the optical low state and probably at least an order of magnitude less in the high state. By contrast, the soft X-ray luminosity increases by an order of magnitude between the optical low and high states. A coronal model or accretion onto the white dwarf can account for the inverse correlation of the soft and hard X-rays.

Fabbiano, G.↗
NASA NTRS1981

Magnetic field of Jupiter: A generalized inverse approach

The estimation of planetary magnetic fields from observations of the magnetic field gathered along a spacecraft flyby trajectory is examined with the aid of generalized inverse techniques, with application to the internal magnetic field of Jupiter. Model nonuniqueness resulting from the limited spatial extent of the observations and noise on the data is explored and quantitative estimates of the model parameter resolution are found. The presence of a substantial magnetic field of external origin due to the currents flowing in the Jovian magnetodisc is found to be an important source of error in estimates of the internal Jovian field, and new models explicitly incorporating these currents are proposed. New internal field models are derived using the vector helium magnetometer observations and the high field fluxgate observations of Pioneer 11, and knowledge of the external current system gained from the Pioneer 10 and Voyagers 1 and 2 encounters.

Connerney, J. E. P.↗
NASA NTRS1981

The magnetic field of Jupiter - A generalized inverse approach

The estimation of planetary magnetic fields from observations of the magnetic field gathered along a spacecraft flyby trajectory is examined with the aid of generalized inverse techniques, with application to the internal magnetic field of Jupiter. Model non-uniqueness resulting from the limited spatial extent of the observations and noise on the data is explored and quantitative estimates of the model parameter resolution are found. The presence of a substantial magnetic field of external origin due to the currents flowing in the Jovian magnetodisc is found to be an important source of error in estimates of the internal Jovian field, and new models explicitly incorporating these currents are proposed. New internal field models are derived using the vector helium magnetometer observations and the high field fluxgate observations of Pioneer 11, and knowledge of the external current system gained from the Pioneer 10 and Voyagers 1 and 2 encounters.

Connerney, J. E. P.↗
NASA NTRS1982

The Jovian ammonia abundance from interferometric observations of limb darkening at 3.4 mm

The relative abundances of the various atomic and molecular constituents in the Jovian atmosphere are important data for studies of the origin of the solar system. The determination of the ammonia abundance presents a number of difficulties. However, difficulties related to a use of the microwave sensing technique can be largely overcome by measuring the brightness distribution across the disk. In particular, information about the atmosphere can be obtained from the degree of limb darkening, which requires only a relative brightness measurement as opposed to an absolute measurement. Valdes and Welch (1978) have used the considered approach in a study of Jupiter at 1.3 cm. In the present investigation a more general relation between the amount of limb darkening in the broad 1.25-cm inversion band of ammonia and the ammonia abundance is derived. The model is applied to new measurements of Jupiter's limb darkening at 3.4 mm.

Valdes, F.↗
NASA NTRS1982

Radio and X-ray structure of Centaurus A

Recent studies of the nearby radio galaxy Centaurus A with the Very Large Array and the Einstein X-Ray Observatory reveal complex radio and X-ray structures. A prominent one-sided jet comprised of resolved knots located 0.2-6 kpc from the nucleus is seen in both radio and X-rays. The X-ray emission is probably synchrotron, requiring in situ reacceleration up to about ten million. Inverse Compton emission is not a likely explanation though a thermal model in which the nucleus ejects dense 100,000 solar mass clouds cannot be excluded. An elongated X-ray region is also found near the 'middle' radio lobe and optical HII regions about 30 kpc NE of the nucleus. Conditions around the active nucleus, the absence of X-rays from the inner radio lobes, and X-ray evidence for a hot interstellar medium are briefly discussed

Feigelson, E. D.↗
NASA NTRS1982

Retrieval of aerosol optical characteristics from polarization measurements of reflected solar radiation above the oceans

The reflected near infrared solar radiation observed from space above the oceans is due mainly to the atmosphere scattering, as the ocean surface is nearly black. The molecular Rayleigh contribution is also minimized at infrared wavelengths and it can be evaluated. It is shown that the degree of polarization is much more sensitive to the aerosol properties than the radiance. Measurements of polarization at two wavelengths and with an angular scanning are simulated and an inversion algorithm is proposed. It aims at finding an 'equivalent aerosol model', which reproduces the optical thickness and the asymmetry factor of the actual aerosol at all wavelengths in the solar spectrum.

Santer, R.↗
NASA NTRS1987

Molecular flow velocity using Doppler shifted Raman spectroscopy

Measurements of molecular flow velocity, static pressure, and translational temperature in the free-stream of a supersonic wind tunnel and behind the shock of a simple model are reviewed. Based on the free-stream demonstration using inverse Raman spectroscopy, an experiment is outlined to investigate the lee-side flow field above a swept delta wing and simulated spectra expected for the leading-edge vortex are included. The extension of the technique to hypersonic wind tunnels is also explored through the use of simulated spectra.

Exton, Reginald J.↗