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NASA NTRS2011

Towards an Optimal Noise Versus Resolution Trade-Off in Wind Scatterometry

A scatterometer is a radar that measures the normalized radar cross section sigma(sup 0) of the Earth's surface. Over the ocean this signal is related to the wind via the geophysical model function (GMF). The objective of wind scatterometry is to estimate the wind vector field from sigma(sup 0) measurements; however, there are many subtleties that complicate this problem-making it difficult to obtain a unique wind field estimate. Conventionally, wind estimation is split into two stages: a wind retrieval stage in which several ambiguous solutions are obtained, and an ambiguity removal stage in which ambiguities are chosen to produce an appropriate wind vector field estimate. The most common approach to wind field estimation is to grid the scatterometer swath into wind vector cells and estimate wind vector ambiguities independently for each cell. Then, field wise structure is imposed on the solution by an ambiguity selection routine. Although this approach is simple and practical, it neglects field wise structure in the retrieval step and does not account for the spatial correlation imposed by the sampling. This makes it difficult to develop a theoretically appropriate noise versus resolution trade-off using pointwise retrieval. Fieldwise structure may be imposed in the retrieval step using a model-based approach. However, this approach is generally only practical if a low order wind field model is applied, which may discard more information than is desired. Furthermore, model-based approaches do not account for the structure imposed by the sampling. A more general fieldwise approach is to estimate all the wind vectors for all the WVCs simultaneously from all the measurements. This approach can account for structure of the wind field as well as structure imposed by the sampling in the wind retrieval step. Williams and Long in 2010 developed a fieldwise retrieval method based on maximum a posteriori estimation (MAP). This MAP approach can be extended to perform a noise versus resolution trade-off, and deal with ambiguity selection. This paper extends the fieldwise MAP estimation approach and investigates both the noise versus resolution trade-off as well as ambiguity removal in the fieldwise wind retrieval step. The method is then applied to the Sea Winds scatterometer and the results are analyzed. This paper extends the fieldwise MAP estimation approach and investigates both the noise versus resolution trade-off as well as ambiguity removal in the fieldwise wind retrieval step. The method is then applied to the Sea Winds scatterometer and the results are analyzed.

soil moisture↗
NASA NTRS1985

The effect of line damping, magneto-optics and parasitic light on the derivation of sunspot vector magnetic fields

The least square fitting of Stokes observations of sunspots using a Milne-Eddington-Unno model appears to lead, in many circumstances, to various inconsistencies such as anomalously large doppler widths and, hence, small magnetic fields which are significantly below those inferred solely from the Zeeman splitting in the intensity profile. It is found that the introduction of additional physics into the model such as the inclusion of damping wings and magneto-optic birefrigence significantly improves the fit to Stokes parameters. Model fits excluding the intensity profile, i.e., of both magnitude as well as spectral shape of the polarization parameters alone, suggest that parasitic light in the intensity profile may also be a source of inconsistencies. The consequences of the physical changes on the vector properties of the field derived from the Fe I lambda 6173 line for the 17 November 1975 spot as well as on the thermodynamic state are discussed. A Doppler width delta lambda (D) - 25mA is bound to be consistent with a low spot temperature and microturbulence, and a damping constant of a = 0.2.

Skumanich, A.↗
NASA NTRS1989

Direct discretization of planar div-curl problems

A control volume method is proposed for planar div-curl systems. The method is independent of potential and least squares formulations, and works directly with the div-curl system. The novelty of the technique lies in its use of a single local vector field component and two control volumes rather than the other way around. A discrete vector field theory comes quite naturally from this idea and is developed. Error estimates are proved for the method, and other ramifications investigated.

Nicolaides, R. A.↗
NASA NTRS1992

Rotational polarities of sudden impulses in the magnetotail lobe

A sudden impulse (SI) is a sudden change in the magnetic field strength which is caused by a change in the solar wind pressure and is observed throughout the magnetosphere. In this report we have examined the rotations of the magnetic field vectors at times of SIs in the magnetotail lobe, by using IMP 6, 7, and 8 magnetometer data. The following properties have been found: (1) at the time of SI the arrowhead of the magnetic vector tends to rotate in one plane; (2) the plane of rotation tends to include the unperturbed magnetic field vector; (3) the plane of rotation tends to be aligned with the radial direction from the magnetotail axis; and (4) the magnetic vectors have a particular rotational polarity: when the plane of rotation is viewed so that the Sun is to the right of the viewed plane and the magnetotail axis is to the bottom, the arrowhead of the vector tends to rotate counterclockwise in this plane. These magnetic vector properties are consistent with those expected when part of an increase in solar wind lateral pressure squeezes the magnetotail axisymmetrically while moving tailward.

Kawano, H.↗
NASA NTRS2008

Split-Block Waveguide Polarization Twist for 220 to 325 GHz

A split-block waveguide circuit that rotates polarization by 90 has been designed with WR-3 input and output waveguides, which are rectangular waveguides used for a nominal frequency range of 220 to 325 GHz. Heretofore, twisted rectangular waveguides equipped with flanges at the input and output have been the standard means of rotating the polarizations of guided microwave signals. However, the fabrication and assembly of such components become difficult at high frequency due to decreasing wavelength, such that twisted rectangular waveguides become impractical at frequencies above a few hundred gigahertz. Conventional twisted rectangular waveguides are also not amenable to integration into highly miniaturized subassemblies of advanced millimeter- and submillimeter-wave detector arrays now undergoing development. In contrast, the present polarization- rotating waveguide can readily be incorporated into complex integrated waveguide circuits such as miniaturized detector arrays fabricated by either conventional end milling of metal blocks or by deep reactive ion etching of silicon blocks. Moreover, the present split-block design can be scaled up in frequency to at least 5 THz. The main step in fabricating a splitblock polarization-rotating waveguide of the present design is to cut channels having special asymmetrically shaped steps into mating upper and lower blocks (see Figure 1). The dimensions of the steps are chosen to be consistent with the WR-3 waveguide cross section, which is 0.864 by 0.432 mm. The channels are characterized by varying widths with constant depths of 0.432, 0.324, and 0.216 mm and by relatively large corner radii to facilitate fabrication. The steps effect both a geometric transition and the corresponding impedance-matched electromagnetic-polarization transition between (1) a WR-3 rectangular waveguide oriented with the electric field vector normal to the block mating surfaces and (2) a corresponding WR-3 waveguide oriented with its electric field vector parallel to the mating surfaces of the blocks. A prototype has been built and tested. Figure 2 presents test results indicative of good performance over nearly the entire WR-3 waveguide frequency band.

Ward, John↗
NASA NTRS1993

Evaluation of two January - June 1992 ERS-1 AMI wind vector data sets

A Jan. - Jun. 1992 10 m height wind vector field was computed with the CMOD2 model function. Freilich and Dunbar used ESA measurements of AMI (Active Microwave Instrument) sigma-naught to derive a refined model function and to produce an alternate Jan. - Jun. 1992 10 m height wind vector field, named FD data. The ESA and FD model functions and algorithms were substantially different. The FD wind vectors were in better agreement with the climatological mean wind field and with moored buoy wind measurements. The average correlation coefficients between monthly mean and daily averaged FD and moored buoy matchups of the Cartesian wind components were 0.84 and 0.74, respectively. The average root mean square differences between the monthly mean and daily averaged FD and moored buoy matchups of the Cartesian wind components were 1.25 and 3.0 m/s, respectively.

Halpern, D.↗
NASA NTRS1997

Magnetic Test Performance Capabilities at the Goddard Space Flight Center as Applied to the Global Geospace Science Initiative

Goddard Space Flight Center's (GSFC) Spacecraft Magnetic Test Facility (SMTF) is a historic test facility that has set the standard for all subsequent magnetic test facilities. The SMTF was constructed in the early 1960's for the purpose of simulating geomagnetic and interplanetary magnetic fields. Additionally, the facility provides the capability for measuring spacecraft generated magnetic fields as well as calibrating magnetic attitude control systems and science magnetometers. The SMTF was designed for large, spacecraft level tests and is currently the second largest spherical coil system in the world. The SMTF is a three-axis Braunbek system composed of four coils on each of three orthogonal axes. The largest coils are 12.7 meters (41.6 feet) in diameter. The three-axis Braunbek configuration provides a highly uniform cancellation of the geomagnetic field over the central 1.8 meter (6 foot) diameter primary test volume. Cancellation of the local geomagnetic field is to within +/-0.2 nanotesla with a uniformity of up to 0.001% within the 1.8 meter (6 foot) diameter primary test volume. Artificial magnetic field vectors from 0-60,000 nanotesla can be generated along any axis with a 0.1 nanotesla resolution. Oscillating or rotating field vectors can also be produced about any axis with a frequency of up to 100 radians/second. Since becoming fully operational in July of 1967, the SMTF has been the site of numerous spacecraft magnetics tests. Spacecraft tested at the SMTF include: the Solar Maximum Mission (SMM), Magsat, LANDSAT-D, the Fast Aurora] Snapshot (FAST) Explorer and the Sub-millimeter-Wave-Astronomy Satellite (SWAS) among others. This paper describes the methodology and sequencing used for the Global Geospace Science (GGS) initiative magnetic testing program in the Goddard Space Flight Center's SMTF. The GGS initiative provides an exemplary model of a strict and comprehensive magnetic control program.

Mitchell, Darryl R.↗
NASA NTRS1977

Lie theoretic aspects of the Riccati equation

Various features of the application of Lie theory to matrix Riccati equations, of basic importance in control and system theories, are discussed. Particular consideration is given to centralizer foliation, the Cartan decomposition, matrix Riccati equations as Lie systems on Grassmanians, local analysis near a zero point of a vector field, linearization in homogeneous space, the tangent bundle in terms of partitioned matrices, and stability properties of fixed points of Riccati vector fields.

Hermann, R.↗
NASA NTRS1990

Bifurcations of relative equilibria

The characteristics of equivariant dynamical systems near relative equilibria (RE: group orbits which are invariant in the flow of an equivariant vector field) are investigated analytically, with a focus on the dynamics and bifurcation (B) behavior. The principles of Lie-group theory are reviewed; the decomposition of the vector field is explained; and particular attention is given to the Bs of RE occurring when an eigenvalue passes through zero, Hopf Bs of RE, the classification of generic secondary steady-state and Hopf Bs with symmetry group O(2), Bs of the zero solution of the Kuramoto-Shivashinsky equation, and possible generic steady-state Bs in the two-dimensional Benard problem. In the latter case, it is shown that the primary generic Bs are to two types of equilibria (hexagons and rolls), while the secondary Bs result in trajectories which are either equilibria or rotating waves.

Krupa, Martin↗
NASA NTRS1981

Studies of high latitude current systems using MAGSAT vector data

The magnetic disturbance fields caused by global external current systems are considered with particular emphasis on improving the understanding of the physical processes which control high latitude current systems. Following processing the MAGSAT data were routinely plotted in the Universal Time (UT) format as well as in a polar plot format. The H'D'U' coordinate system, was adopted as the standard for representing the MAGSAT residual magnetic field vectors. A data file was generated and the TPOLAR computer code was developed to determine from the orbital elements, the time, latitude, and MLT of the extremum latitude of each transpolar segment of orbit. The precision of the vector data set from MAGSAT prompted an extended exploratory phase for data analysis procedures, modeling techniques and phenomenology.

Burrows, J. R.↗
NASA NTRS1981

Alternative formulations of magnetospheric plasma electrodynamics

The fundamental equations of magnetospheric plasma electrodynamics are considered from a theoretical standpoint that stresses the basic equivalence of various seemingly different formal representations. The mathematical properties of vector fields are reviewed, and their implications in electrodynamics are studied. The irrotational and solenoidal parts of the electric field are associated with two physically distinct types of sources. Relativistic covariance and gauge invariance in electromagnetic theory are reviewed and discussed in the context of an approach in which the mathematical properties of vector fields are taken as primary concepts. Special attention is given to the use and interpretation of the Coulomb gauge potential functions. This choice of gauge is sometimes regarded with undue suspicion, possibly because of a certain paradox concerning causality. The paradox is discussed and resolved. Useful properties of the Coulomb gauge are identified. These need not be limited to the case of slow time variations and can extend beyond the limits of validity of ideal MHD theory.

Cragin, B. L.↗
NASA NTRS1985

The seasonal variation of the D region as inferred from propagation characteristics of LF radio waves

The propagation data of JG2AS 40 kHz (Japanese Standard Frequency), Loran C 100 kHz radio waves, and meteorological data were analyzed to study the association of propagation characteristics of LF radio waves with the atmospheric circulation in the mesosphere. The monthly averaged electric fields were depicted on the complex plane for typical summer and winter months, June and November. The locus traced out by the electric field vector during daytime is nearly circular. This is because during daytime the amplitude of the sky wave remains nearly constant while its phase changes in accord with the height change of the reflection layer, and thus the electric field vector traces out a circular locus with its center at the tip of the supposed ground wave vector. The locus has a loop during the sunrise or sunset period, which seems to arise from interference of two waves reflected by two different layers. In June the amplitude of the sky wave decreases rapidly before the dawn or increases after the dusk. In November such rapid change is not observed. During nighttime, the sky wave phase changes in such a way as to suggest that the reflection height moves upwards with time before midnight or lowers after midnight in November. In June it changes similarly before midnight, but after midnight it varies erratically. These characteristics are closely related to the structure of the D region, which is clearly shown by simulating the loci traced out by electric fields.

Ishimine, T.↗
NASA NTRS1986

Flare activity, sunspot motions, and the evolution of vector magnetic fields in Hale region 17244

The magnetic and dynamical circumstances leading to the 1B/M4 flare of November 5, 1980 are studied, and a strong association is found between the buildup of magnetic shear and the onset of flare activity within the active region. The development of shear, as observed directly in vector magnetograms, is consistent in detail with the dynamical history of the active region and identifies the precise location of the optical and hard-X-ray kernels of the flare emission.

Neidig, Donald F.↗
NASA NTRS1980

Hamiltonian indices and rational spectral densities

Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.

Byrnes, C. I.↗
NASA NTRS1990

Surface representations of two- and three-dimensional fluid flow topology

We discuss our work using critical point analysis to generate representations of the vector field topology of numerical flow data sets. Critical points are located and characterized in a two-dimensional domain, which may be either a two-dimensional flow field or the tangential velocity field near a three-dimensional body. Tangent curves are then integrated out along the principal directions of certain classes of critical points. The points and curves are linked to form a skeleton representing the two-dimensional vector field topology. When generated from the tangential velocity field near a body in a three-dimensional flow, the skeleton includes the critical points and curves which provide a basis for analyzing the three-dimensional structure of the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations to generate surfaces representing the topology of the associated flow separations.

Helman, James L.↗
NASA NTRS1977

On the alignment of plasma anisotropies and the magnetic field direction in the solar wind

One year's Imp 6 solar wind plasma and magnetic field data are examined to determine whether anisotropies in particle velocity distributions are aligned with the measured interplanetary magnetic field vector. Alignment of components in the analysis plane was generally found to be excellent whenever plasma parameter magnitudes were larger than determination uncertainties, although some spread exists (typical rms approximately equal to 10 deg). By assuming cylindrical symmetry about the simultaneously measured magnetic field vector during the 1-year interval under study, three-dimensional values of selected solar wind plasma thermal parameters were constructed from the two-dimensional plasma measurements, and the statistical properties of their distributions have been tabulated.

Asbridge, J. R.↗
NASA NTRS1985

Effect of polarized radiative transfer on the Hanle magnetic field determination in prominences: Analysis of hydrogen H alpha line observations at Pic-du-Midi

The linear polarization of the Hydrogen H alpha line of prominences has been computed, taking into account the effect of a magnetic field (Hanle effect), of the radiative transfer in the prominence, and of the depolarization due to collisions with the surrounding electrons and protons. The corresponding formalisms are developed in a forthcoming series of papers. In this paper, the main features of the computation method are summarized. The results of computation have been used for interpretation in terms of magnetic field vector measurements from H alpha polarimetric observations in prominences performed at Pic-du-Midi coronagraph-polarimeter. Simultaneous observations in one optically thin line (He I D(3)) and one optically thick line (H alpha) give an opportunity for solving the ambiguity on the field vector determination.

Bommier, V.↗
NASA NTRS1994

Multipole moments of stellar oscillation modes

The oscillating mass 2(exp l)-pole moment, M(sub nl), of a star in a given (normalized) oscillation mode determines the energy that can be absorbed by the mode in a tidal interaction and the power radiated by the mode in gravitational waves, both of which are proportional to (absolute value of M(sub nl))(exp 2). The coefficients in the expansion of the vector fields del(r(exp l)Y(sub lm)(theta, phi)) in terms of the displacement fields of modes of given l and m are proportional to M(sub nl). This expansion leads to a sum rule sum over n(absolute value of M(sub nl))(exp 2) = constant. For stars of weak to moderate central condensation (such as neutron stars), the f-mode is well approximated by the vector field being expanded, and therefore it takes the lion's share of the sum. Thus the multipole moments of all other modes must be small. In there numerical evaluation, it is necessary to know the shape of the eigenfunctions quite precisly, since a small f-mode contamination can significantly increase the obtained values. This contamination occurs in some `hybrid' numerical computations of neutron star oscillations with relativistic equilibrium stars and Newtonian dynamics (e.g., McDermott et al. 1988). In this case, it is due to a slight inconsistency in the models and leads to a large overestimate of the power radiated in gravitational waves by modes other than the f-mode, although their oscillation periods are nearly unaffected.

Reisenegger, Andreas↗