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Reliability of CHAMP Anomaly Continuations

CHAMP is recording state-of-the-art magnetic and gravity field observations at altitudes ranging over roughly 300 - 550 km. However, anomaly continuation is severely limited by the non-uniqueness of the process and satellite anomaly errors. Indeed, our numerical anomaly simulations from satellite to airborne altitudes show that effective downward continuations of the CHAMP data are restricted to within approximately 50 km of the observation altitudes while upward continuations can be effective over a somewhat larger altitude range. The great unreliability of downward continuation requires that the satellite geopotential observations must be analyzed at satellite altitudes if the anomaly details are to be exploited most fully. Given current anomaly error levels, joint inversion of satellite and near- surface anomalies is the best approach for implementing satellite geopotential observations for subsurface studies. We demonstrate the power of this approach using a crustal model constrained by joint inversions of near-surface and satellite magnetic and gravity observations for Maude Rise, Antarctica, in the southwestern Indian Ocean. Our modeling suggests that the dominant satellite altitude magnetic anomalies are produced by crustal thickness variations and remanent magnetization of the normal polarity Cretaceous Quiet Zone.

vonFrese, Ralph R. B.

On the Measurement of Elemental Abundance Ratios in Inner Galaxy H II Regions

Although abundance gradients in the Milky Way Galaxy certainly exist, details remain uncertain, particularly in the inner Galaxy, where stars and H II regions in the Galactic plane are obscured optically. In this paper we revisit two previously studied, inner Galaxy H II regions: G333.6-0.2 and W43. We observed three new positions in G333.6-0.2 with the Kuiper Airborne Observatory and reobserved the central position with the Infrared Space Observatory's Long Wavelength Spectrometer in far-infrared lines of S++, N++, N+, and O++. We also added the N+ lines at 122 and 205 microns to the suite of lines measured in W43 by Simpson et al.. The measured electron densities range from approx. 40 to over 4000 per cu cm in a single HII region, indicating that abundance analyses must consider density variations, since the critical densities of the observed lines range from 40 to 9000 per cu cm. We propose a method to handle density variations and make new estimates of the S/H and N/H abundance ratios. We find that our sulfur abundance estimates for G333.6-0.2 and W43 agree with the S/H abundance ratios expected for the gradient previously reported by Simpson et al., with the S/H values revised to be smaller owing to changes in collisional excitation cross sections. The estimated N/H, S/H, and N/S ratios are the most reliable because of their small corrections for unseen ionization states (< or approx. 10%). The estimated N/S ratios for the two sources are smaller than what would be calculated from the N/H and S/H ratios in our previous paper. If all low excitation H II regions had similar changes to their N/S ratios as a result of adding measurements of N+ to previous measurements of N++, there would be no or only a very small gradient in N/S. This is interesting because nitrogen is considered to be a secondary element and sulfur is a primary element in galactic chemical evolution calculations. We compute models of the two H II regions to estimate corrections for the other unseen ionization states. We find, with large uncertainties, that oxygen does not, have a high abundance, with the result that the N/O ratio is as high (approx. 0.35) as previously reported. The reasons for the uncertainty in the ionization corrections for oxygen are both the non-uniqueness of the H II region models and the sensitivity of these models to different input atomic data and stellar atmosphere models. We discuss these predictions and conclude that only a few of the latest models adequately reproduce H II region observations, including the well-known, relatively-large observed Ne++/O++ ratios in low- and moderate-excitation H II regions.

Simpson, Janet P.

Meridional Variations of C2H2 and C2H6 in Jupiter's Atmosphere from Cassini CIRS Infrared Spectra

Hydrocarbons such as acetylene (C2H2) and ethane (C2H6) are important tracers in Jupiter's atmosphere, constraining our models of the chemical and dynamical processes. However, our knowledge of the vertical and meridional variations of their abundances has remained sparse. During the flyby of the Cassini spacecraft in December 2000, the Composite Infrared Spectrometer (CIRS) instrument was used to map the spatial variation of emissions from 10-1400 cm(sup -1) (1000-7 microns). In this paper we analyze a zonally-averaged set of CIRS spectra taken at the highest (0.5 cm(sup -1)) resolution, to infer atmospheric temperatures in the stratosphere at 0.5-20 mbar via the v4 band of CH4, and in the troposphere at 150-400 mbar, via the H2 absorption at 600-800 cm(sup -1). Simultaneously, we retrieve the abundances of C2H2 and C2H6 via the v5 and vg bands respectively. Tropospheric absorption and stratospheric emission are highly anti-correlated at the CIRS resolution, introducing a non-uniqueness into the retrievals, such that vertical gradient and column abundance cannot both be found without additional constraints. Assuming profile gradients from photochemical calculations, we show that the column abundance of C2H2 decreases sharply towards the poles by a factor approximately 4, while C2H6 is unchanged in the north and increasing in the south, by a factor approximately 1.8. An explanation for the meridional trends is proposed in terms of a combination of photochemistry and dynamics. Poleward, the decreasing UV flux is predicted to decrease the abundances of C2H2 and C2H6 by factors 2.7 and 3.5 respectively at a latitude 70 deg. However, the lifetime of C2H6 in the stratosphere (5 x 10(exp 9)) is much longer than the dynamical timescale for meridional motions inferred from SL-9 debris (5 x 10(exp 8 s)), and therefore the constant or rising abundance towards high latitudes likely indicates that meridional mixing dominates over photochemical effects. For C2H2, the opposite occurs, with the relatively short photochemical lifetime (3 x 10(exp 7 s)), compared to meridional mixing times, ensuring that the expected photochemical trends are visible.

Nixon, C. A.

Meridional Variations of C2H2 and C2H6 in Jupiter's Atmosphere from Cassini CIRS Infrared Spectra

The abundances of hydrocarbons such as acetylene (C2H2) and ethane (C2H6) in Jupiter's atmosphere are important physical quantities, constraining our models of the chemical and dynamical processes. However, our knowledge of these quantities and their vertical and latitudinal variations has remained sparse. The flyby of the Cassini spacecraft with Jupiter at the end of 2000 provided an excellent opportunity to observe the infrared spectrum with the Composite Infrared Spectrometer (CIRS) instrument, mapping the spatial variation of emissions from 10-1400 cm-1. CIRS spectra taken at the highest resolution (0.5 cm-1) in early December 2000 have been analysed to infer atmospheric temperatures in the stratosphere at 0.5-20 mbar via the v4 of CH4, and in the troposphere at 100-400 mbar, via the hydrogen collision-induced continuum absorption at 600-800 cm. Simultaneously, we have searched for meridional abundance variations in C2H2 and C2H6 via the v5 and vg bands respectively. Tropospheric absorption and stratospheric emission are highly anti-correlated at the CIM resolution, introducing a non-uniqueness into the retrievals, which means that vertical gradient and column abundance cannot be simultaneously found without additional constraints. If we assume the profile shapes from photochemical model calculations, we show that the column abundance of C2H2 must decrease sharply towards the poles, while C2H6 is constant or slightly increasing. The relevance of these results to current photochemical and dynamical knowledge of Jupiter's atmosphere is discussed.

Nixon, C. A.

A Microphysically-based Approach to Inferring Porosity, Grain Size, and Dust Abundance in the Seasonal Caps from Atmospherically-corrected TES Spectra

One of the highlights of the TES observations in the polar regions has been the identification of a "cryptic" region in the south where CO2 appears to be in the form of a solid slab rather than a fluffy frost. While the exact mechanism(s) by which the cryptic region is formed are still subject of some debate, it appears certain that a type of rapid metamorphism related to the high volatility of CO2 ice is involved. The high volatility of CO2 ice under martian conditions has several Solar System analogs (N2 on Triton and Pluto, SO2 on Io), thus making the martian cryptic region somewhat less cryptic and certainly non-unique among planetary objects. In an endmember scenario, both the formation and the spectral properties of the cryptic region (and of other areas in the seasonal caps) can be quantitatively modeled by considering sintering of an ensemble of quasi-spherical CO2 grains. This model includes the special case of instanteneous slab formation, which occurs when the grains are sufficiently small (in the submicron range) so that their sintering timescale is short relative to the deposition timescale (a situation analogous to the "sintering" of water droplets falling into a pond).

Eluszkiewicz, J.

Closed Loop System Identification with Genetic Algorithms

High performance control design for a flexible space structure is challenging since high fidelity plant models are di.cult to obtain a priori. Uncertainty in the control design models typically require a very robust, low performance control design which must be tuned on-orbit to achieve the required performance. Closed loop system identi.cation is often required to obtain a multivariable open loop plant model based on closed-loop response data. In order to provide an accurate initial plant model to guarantee convergence for standard local optimization methods, this paper presents a global parameter optimization method using genetic algorithms. A minimal representation of the state space dynamics is employed to mitigate the non-uniqueness and over-parameterization of general state space realizations. This control-relevant system identi.cation procedure stresses the joint nature of the system identi.cation and control design problem by seeking to obtain a model that minimizes the di.erence between the predicted and actual closed-loop performance.

Whorton, Mark S.

On the Inversion for Mass (Re)Distribution from Global (Time-Variable) Gravity Field

The well-known non-uniqueness of the gravitational inverse problem states the following: The external gravity field, even if completely and exactly known, cannot Uniquely determine the density distribution of the body that produces the gravity field. This is an intrinsic property of a field that obeys the Laplace equation, as already treated in mathematical as well as geophysical literature. In this paper we provide conceptual insight by examining the problem in terms of spherical harmonic expansion of the global gravity field. By comparing the multipoles and the moments of the density function, we show that in 3-S the degree of knowledge deficiency in trying to inversely recover the density distribution from external gravity field is (n+l)(n+2)/2 - (2n+l) = n(n-1)/2 for each harmonic degree n. On the other hand, on a 2-D spherical shell we show via a simple relationship that the inverse solution of the surface density distribution is unique. The latter applies quite readily in the inversion of time-variable gravity signals (such as those observed by the GRACE space mission) where the sources over a wide range of the scales largely come from the Earth's Surface.

Chao, Benjamin F.

Aerosol properties computed from aircraft-based observations during the ACE- Asia campaign: A case study of lidar ratio closure and aerosol radiative effects - 2

For a vertical profile with three distinct layers (marine boundary, pollution and dust), observed during the ACE-Asia campaign, we carried out a comparison between the modeled lidar ratio vertical profile and that obtained from collocated airborne NASA AATS-14 sunphotometer and shipborne Micro-Pulse Lidar (MPL) measurements. Vertically resolved lidar ratio was calculated from two size distribution vertical profiles - one obtained by inversion of sunphotometer-derived extinction spectra, and one measured in-situ - combined with the same refractive index model based on aerosol chemical composition. The aerosol model implies single scattering albedos of 0.78 - 0.81 and 0.93 - 0.96 at 0.523 microns (the wavelength of the lidar measurements), in the pollution and dust layers, respectively. The lidar ratios calculated from the two size distribution profiles have close values in the dust layer; they are however, significantly lower than the lidar ratios derived from combined lidar and sunphotometer measurements, most probably due to the use of a simple nonspherical model with a single particle shape in our calculations. In the pollution layer, the two size distribution profiles yield generally different lidar ratios. The retrieved size distributions yield a lidar ratio which is in better agreement with that derived from lidar/sunphotometer measurements in this layer, with still large differences at certain altitudes (the largest relative difference was 46%). We explain these differences by non-uniqueness of the result of the size distribution retrieval and lack of information on vertical variability of particle refractive index. Radiative transfer calculations for this profile showed significant atmospheric radiative forcing, which occurred mainly in the pollution layer. We demonstrate that if the extinction profile is known then information on the vertical structure of absorption and asymmetry parameter is not significant for estimating forcing at TOA and the surface, while it is of importance for estimating vertical profiles of radiative forcing and heating rates.

Kuzmanoski, Maja

Lightning Charge Retrievals: Dimensional Reduction, LDAR Constraints, and a First Comparison with LIS Satellite Data

A "dimensional reduction" (DR) method is introduced for analyzing lightning field changes (DELTAEs) whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight (x, y, z, Q, x', y', z', Q') to just four (x, y, z, Q). The four unknowns (x, y, z, Q) are found by performing a numerical minimization of a chi-square function. At each step of the minimization, an Overdetermined Fixed Matrix (OFM) method is used to immediately retrieve the best "residual source" (x', y', z', Q'), given the values of (x, y, z, Q). In this way, all 8 parameters (x, y, z, Q, x', y', z', Q') are found, yet a numerical search of only 4 parameters (x, y, z, Q) is required. The DR method has been used to analyze lightning-caused DeltaEs derived from multiple ground-based electric field measurements at the NASA Kennedy Space Center (KSC) and USAF Eastern Range (ER). The accuracy of the DR method has been assessed by comparing retrievals with data provided by the Lightning Detection And Ranging (LDAR) system at the KSC-ER, and from least squares error estimation theory, and the method is shown to be a useful "stand-alone" charge retrieval tool. Since more than one charge distribution describes a finite set of DELTAEs (i.e., solutions are non-unique), and since there can exist appreciable differences in the physical characteristics of these solutions, not all DR solutions are physically acceptable. Hence, an alternative and more accurate method of analysis is introduced that uses LDAR data to constrain the geometry of the charge solutions, thereby removing physically unacceptable retrievals. The charge solutions derived from this method are shown to compare well with independent satellite- and ground-based observations of lightning in several Florida storms.

Koshak, W. J.

Distributed antenna system and method

System and methods are disclosed for employing one or more radiators having non-unique phase centers mounted to a body with respect to a plurality of transmitters to determine location characteristics of the body such as the position and/or attitude of the body. The one or more radiators may consist of a single, continuous element or of two or more discrete radiation elements whose received signals are combined. In a preferred embodiment, the location characteristics are determined using carrier phase measurements whereby phase center information may be determined or estimated. A distributed antenna having a wide angle view may be mounted to a moveable body in accord with the present invention. The distributed antenna may be utilized for maintaining signal contact with multiple spaced apart transmitters, such as a GPS constellation, as the body rotates without the need for RF switches to thereby provide continuous attitude and position determination of the body.

Fink, Patrick W.

Apparent Transition Behavior of Widely-Used Turbulence Models

The Spalart-Allmaras and the Menter SST k-omega turbulence models are shown to have the undesirable characteristic that, for fully turbulent computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart-Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause non-uniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a higher freestream turbulence level or by making a simple change to one of the model constants. Two-equation k-omega models, including the SST model, exhibit strong sensitivity to numerical resolution near the area where turbulence initiates. Thus, inconsistent apparent transition behavior with grid refinement in this case does not appear to stem from the presence of a degenerate fixed point. Rather, it is a fundamental property of the k-omega model itself, and is not easily remedied.

Rumsey, Christopher L.

In Search of Multi-Peaked Reflective Spectrum with Optic Fiber Bragg Grating Sensor for Dynamic Strain Measurement

In a typical optic fiber Bragg grating (FBG) strain measurement, unless in an ideal static laboratory environment, the presence of vibration or often disturbance always exists, which often creates spurious multiple peaks in the reflected spectrum, resulting in a non-unique determination of strain value. In this report we attempt to investigate the origin of this phenomenon by physical arguments and simple numerical simulation. We postulate that the fiber gratings execute small amplitude transverse vibrations changing the optical path in which the reflected light traverses slightly and non-uniformly. Ultimately, this causes the multi-peak reflected spectrum.

Tai, Hsiang

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

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Nguyen, Nhan T.

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

Image Correlation Pattern Optimization for Micro-Scale In-Situ Strain Measurements

The accuracy and precision of digital image correlation (DIC) is a function of three primary ingredients: image acquisition, image analysis, and the subject of the image. Development of the first two (i.e. image acquisition techniques and image correlation algorithms) has led to widespread use of DIC; however, fewer developments have been focused on the third ingredient. Typically, subjects of DIC images are mechanical specimens with either a natural surface pattern or a pattern applied to the surface. Research in the area of DIC patterns has primarily been aimed at identifying which surface patterns are best suited for DIC, by comparing patterns to each other. Because the easiest and most widespread methods of applying patterns have a high degree of randomness associated with them (e.g., airbrush, spray paint, particle decoration, etc.), less effort has been spent on exact construction of ideal patterns. With the development of patterning techniques such as microstamping and lithography, patterns can be applied to a specimen pixel by pixel from a patterned image. In these cases, especially because the patterns are reused many times, an optimal pattern is sought such that error introduced into DIC from the pattern is minimized. DIC consists of tracking the motion of an array of nodes from a reference image to a deformed image. Every pixel in the images has an associated intensity (grayscale) value, with discretization depending on the bit depth of the image. Because individual pixel matching by intensity value yields a non-unique scale-dependent problem, subsets around each node are used for identification. A correlation criteria is used to find the best match of a particular subset of a reference image within a deformed image. The reader is referred to references for enumerations of typical correlation criteria. As illustrated by Schreier and Sutton and Lu and Cary systematic errors can be introduced by representing the underlying deformation with under-matched shape functions. An important implication, as discussed by Sutton et al., is that in the presence of highly localized deformations (e.g., crack fronts), error can be reduced by minimizing the subset size. In other words, smaller subsets allow the more accurate resolution of localized deformations. Contrarily, the choice of optimal subset size has been widely studied and a general consensus is that larger subsets with more information content are less prone to random error. Thus, an optimal subset size balances the systematic error from under matched deformations with random error from measurement noise. The alternative approach pursued in the current work is to choose a small subset size and optimize the information content within (i.e., optimizing an applied DIC pattern), rather than finding an optimal subset size. In the literature, many pattern quality metrics have been proposed, e.g., sum of square intensity gradient (SSSIG), mean subset fluctuation, gray level co-occurrence, autocorrelation-based metrics, and speckle-based metrics. The majority of these metrics were developed to quantify the quality of common pseudo-random patterns after they have been applied, and were not created with the intent of pattern generation. As such, it is found that none of the metrics examined in this study are fit to be the objective function of a pattern generation optimization. In some cases, such as with speckle-based metrics, application to pixel by pixel patterns is ill-conditioned and requires somewhat arbitrary extensions. In other cases, such as with the SSSIG, it is shown that trivial solutions exist for the optimum of the metric which are ill-suited for DIC (such as a checkerboard pattern). In the current work, a multi-metric optimization method is proposed whereby quality is viewed as a combination of individual quality metrics. Specifically, SSSIG and two auto-correlation metrics are used which have generally competitive objectives. Thus, each metric could be viewed as a constraint imposed upon the others, thereby precluding the achievement of their trivial solutions. In this way, optimization produces a pattern which balances the benefits of multiple quality metrics. The resulting pattern, along with randomly generated patterns, is subjected to numerical deformations and analyzed with DIC software. The optimal pattern is shown to outperform randomly generated patterns.

Bomarito, G. F.

Thermophysical Properties Along Curiosity's Traverse in Gale Crater, Mars, Derived from the REMS Ground Temperature Sensor

The REMS instrument onboard the Mars Science Laboratory rover, Curiosity, has measured ground temperature nearly continuously at hourly intervals for two Mars years. Coverage of the entire diurnal cycle at 1 Hz is available every few martian days. We compare these measurements with predictions of surface atmosphere thermal models to derive the apparent thermal inertia and thermally derived albedo along the rovers traverse after accounting for the radiative effects of atmospheric water ice during fall and winter, as is necessary to match the measured seasonal trend. The REMS measurements can distinguish between active sand, other loose materials, mudstone, and sandstone based on their thermophysical properties. However, the apparent thermal inertias of bedrock dominated surfaces [approx. 350-550 J m(exp. -2) K(exp. -1 s(exp. -1/2 )] are lower than expected. We use rover imagery and the detailed shape of the diurnal ground temperature curve to explore whether lateral or vertical heterogeneity in the surface materials within the sensor footprint might explain the low inertias. We find that the bedrock component of the surface can have a thermal inertia as high as 650-1700 J m(exp. -2) K(exp. -1) s(exp. -1/2) for mudstone sites and approx. 700 J m(exp. -2) K(exp. -1) s(exp. - 1/2) for sandstone sites in models runs that include lateral and vertical mixing. Although the results of our forward modeling approach may be non-unique, they demonstrate the potential to extract information about lateral and vertical variations in thermophysical properties from temporally resolved measurements of ground temperature.

Vasavada, Ashwin R.

Development of an SE(3)-based Rigid Body Pose Estimation Scheme for Unknown Moments of Inertia in a Spacecraft

In real-world applications, the consideration of state and parameter uncertainties is an important part of any navigation and control system. Uncertainties can arise because of the instruments, communication systems, or external disturbances. Parameter uncertainty can be due to uncertainties in the data or the calibration process used. The objective of this research is to develop a rigid body pose estimation scheme on nonlinear manifolds of rigid body motion groups for unknown mass properties moments of inertia with application in space launch. An unscented Kalman filter is developed on special Euclidean space and their tangent bundle to address uncertainties in the states and inertia properties. This estimator accounts for uncertainties, while considering rotational-translational coupling, and avoids singularity or non-uniqueness issues. Since this estimator is based on the nonlinear manifolds on which rigid body motion evolves, it is reliable and is expected to result in high level of accuracy. The estimators are validated on a generic model of Logistic Module (LM) and a cuboid spacecraft model. The algorithms can then be tested on Dragon XL, HTV-X, and possibly other spacecraft.

Moments of Inertia