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At least 415 records · Page 23

Improvement of Raman lidar algorithm for quantifying aerosol extinction

Aerosols are particles of different composition and origin and influence the formation of clouds which are important in atmospheric radiative balance. At the present there is high uncertainty on the effect of aerosols on climate and this is mainly due to the fact that aerosol presence in the atmosphere can be highly variable in space and time. Monitoring of the aerosols in the atmosphere is necessary to better understanding many of these uncertainties. A lidar (an instrument that uses light to detect the extent of atmospheric aerosol loading) can be particularly useful to monitor aerosols in the atmosphere since it is capable to record the scattered intensity as a function of altitude from molecules and aerosols. One lidar method (the Raman lidar) makes use of the different wavelength changes that occur when light interacts with the varying chemistry and structure of atmospheric aerosols. One quantity that is indicative of aerosol presence is the aerosol extinction which quantifies the amount of attenuation (removal of photons), due to scattering, that light undergoes when propagating in the atmosphere. It can be directly measured with a Raman lidar using the wavelength dependence of the received signal. In order to calculate aerosol extinction from Raman scattering data it is necessary to evaluate the rate of change (derivative) of a Raman signal with respect to altitude. Since derivatives are defined for continuous functions, they cannot be performed directly on the experimental data which are not continuous. The most popular technique to find the functional behavior of experimental data is the least-square fit. This procedure allows finding a polynomial function which better approximate the experimental data. The typical approach in the lidar community is to make an a priori assumption about the functional behavior of the data in order to calculate the derivative. It has been shown in previous work that the use of the chi-square technique to determine the most likely functional behavior of the data prior to actually calculating the derivative eliminates the need for making a priori assumptions. We note that the a priori choice of a model itself can lead to larger uncertainties as compared to the method that is validated here. In this manuscript, the chi-square technique that determines the most likely functional behavior is validated through numerical simulation and by application to a large body of Raman lidar measurements. In general, we show that the chi-square approach to evaluate aerosol extinction yields lower extinction uncertainty than the traditional technique. We also use the technique to study the feasibility of developing a general characterization of the extinction uncertainty that could permit the uncertainty in Raman lidar aerosol extinction measurements to be estimated accurately without the use of the chi-square technique.

Russo, Felicita↗

An a priori model for the reduction of nutation observations: KSV(1994.3) nutation series

We discuss the formulation of a new nutation series to be used in the reduction of modern space geodetic data. The motivation for developing such a series is to develop a nutation series that has smaller short period errors than the IAU 1980 nutation series and to provide a series that can be used with techniques such as the Global Positioning System (GPS) that have sensitivity to nutations but can directly separate the effects of nutations from errors in the dynamical force models that effect the satellite orbits. A modern nutation series should allow the errors in the force models for GPS to be better understood. The series is constructed by convolving the Kinoshita and Souchay rigid Earth nutation series with an Earth response function whose parameters are partly based on geophysical models of the Earth and partly estimated from a long series (1979-1993) of very long baseline interferometry (VLBI) estimates of nutation angles. Secular rates of change of the nutation angles to represent corrections to the precession constant and a secular change of the obliquity of the ecliptic are included in the theory. Time dependent amplitudes of the Free Core Nutation (FCN) that is most likely excited by variations in atmospheric pressure are included when the geophysical parameters are estimated. The complex components of the prograde annual nutation are estimated simultaneously with the geophysical parameters because of the large contribution to the nutation from the S(sub 1) atmospheric tide. The weighted root mean square (WRMS) scatter of the nutation angle estimates about this new model are 0.32 mas and the largest correction to the series when the amplitudes of the ten largest nutations are estimated is 0.18 +/- 0.03 mas for the in phase component of the prograde 18. 6 year nutation.

Herring, T. A.↗

Optimization Simulations for a Gamma-Ray Calibration Standard for a Cyclic Neutron Activation Analysis Pneumatic System at the Penn State Breazeale Reactor

For new experimental setups, the initial testing and calibrations can be expensive and time consuming without prior optimization. However, these issues can be mitigated using realistic modeling and simulation studies of the proposed system a priori. Specifically, an experiment can be performed virtually using realistic simulations and the expected results evaluated to inform adjustments of the experimental setup to achieve optimum results. At the Penn State Breazeale Reactor, a new pneumatic transfer system has been developed for the detection and characterization of short-lived fission fragments to enhance and complement existing nuclear data. The system accomplishes this task by transporting samples cyclically between an assortment of gamma-ray/neutron detectors and the reactor-core vicinity with sub-second transit times. The measured neutron flux paired with simulations of detector response using Geant4 and a custom module for estimating cascade summing effects and corrections were used to select sample-material masses for system characterization. With the optimized sample masses, an experimental counting plan for characterizing the repeatability of the newly developed pneumatic system was developed. Finally, the predictions made with these simulations allowed for optimization of the irradiation sample characteristics and gamma-ray detection system.

cyclic neutron activation, gamma-ray spectroscopy↗

Understanding Differences Between Co-Incident CloudSat, Aqua/MODIS and NOAA18 MHS Ice water Path Retrievals Over the Tropical Oceans

Accurate measurement of the physical and radiative properties of clouds and their representation in climate models continues to be a challe nge. Model parameterizations are still subject to a large number of t unable parameters; furthermore, accurate and representative in situ o bservations are very sparse, and satellite observations historically have significant quantitative uncertainties, particularly with respect to particle size distribution (PSD) and cloud phase. Ice Water Path (IWP), or amount of ice present in a cloud column, is an important cl oud property to accurately quantify, because it is an integral measur e of the microphysical properties of clouds and the cloud feedback pr ocesses in the climate system. This paper investigates near co-incident retrievals of IWP over tropical oceans using three diverse measurem ent systems: radar from CloudSat, Vis/IR from Aqua/MODIS, and microwa ve from NOAA-18IMHS. CloudSat 94 GHz radar measurements provide high resolution vertical and along-orbit structure of cloud reflectivity a nd enable IWP (and IWC) retrievals. Overlapping MODIS measurements of cloud optical thickness and phase allow estimates of IWP when cloud tops are identified as being ice. Periodically, NOAA18 becomes co-inci dent in space I time to enable comparison of A-Train measurements to IWP inferred from the 157 and 89 GHz channel radiances. This latter m easurement is effective only for thick convective anvil systems. We s tratify these co-incident data (less than 4 minutes separation) into cirrus only, cirrus overlying liquid water clouds, and precipitating d eep convective clouds. Substantial biases in IWP and ice effective ra dius are found. Systematic differences in these retrievals are consid ered in light of the uncertainties in a priori assumptions ofPSDs, sp ectral sensitivity and algorithm strategies, which have a direct impact on the IWP product.

Pittman, Jasna↗

20-Years of Atmospheric Temperature, Water Vapor, Cloud, and Surface Temperature Anomalies and Trends Derived From Operational Hyperspectral Ir Sounders

Hyperspectral IR sounders such as AIRS on Aqua, CrIS on S-NPP, NOAA20 and JPSS-2, IASI on Metop A, B, and C provide high-quality atmospheric temperature, water, vapor, and greenhouse gas vertical profiles. Additionally, they provide atmospheric cloud properties, surface emissivity, and surface skin temperatures. We have developed two algorithms which can consistently derive these products from multiple IR sounders. The first one is a Single Field-of-view Sounder Atmospheric Product (SIFSAP) algorithm and the second one is a Climate Fingerprinting Sounder Product (ClimFiSP) algorithm. Compared to current operational AIRS and CrIS Level-2 (L2) algorithms, which perform one retrieval for each 3 by 3 field of views (FOVs) using a cloud-clearing approach, the SiFSAP algorithm, on the other hand, performs one retrieval for each FOV using an all-sky optimal estimation approach. The SiFSAP algorithm retrieves all the above-mentioned atmosphere and surface properties simultaneously including cloud properties with 3-time higher spatial resolution and 9-times more products. The core of the SiFSAP algorithm is an accurate and fast Principal Component-based Radiative Transfer Model (PCRTM), which can calculate hyperspectral radiance spectra under both clear and cloudy conditions. The PCRTM was developed in the past decade using consistent reference line-by-line radiative transfer model and spectroscopy for hyperspectral sounders such as AIRS, CrIS, IASI, NAST-I, and S-HIS. The SiFSAP retrieval algorithm also uses the same climatology a priori and associated covariances, which makes it ideal for generating high quality products for both weather and climate applications. Climate products are typically derived by performing spatial and temporal averaging of L2 products. It is a time-consuming process to generate L2 data products since AIRS, CrIS, and IASI have millions of observations each day with thousands of spectral channels for each observation. Additionally, differences in L2 retrieval algorithms for different satellite sensors can lead to errors in the climate products. Our ClimFiSP algorithm, which performs retrievals from spatiotemporally averaged L1 hyperspectral radiances directly, will be orders of magnitude faster than traditional method. he ClimFiSP algorithm uses consistent radiative kernels and a robust spectral fingerprinting method. It provides accurate data climate data fusion products from multiple satellite sensors. We have applied this method to both AIRS and CrIS (on SNPP and on NOAA 20) data and generated two decades climate data records for atmospheric temperature, water vapor, cloud, trace gases, and surface skin temperature. Both SiFSAP and ClimFiSP will be available at NASA GES DISC data center for public access.

Xu Liu↗

A Historical Overview of the NASA Orbital Debris Program Office’s Laboratory Optical Measurements

The NASA Orbital Debris Program Office (ODPO) has used laboratory measurements to help bring ground-based measurements together with models to ascertain Earth-orbiting target parameters of interest to support various orbital debris models. In 2005, the Optical Measurement Center (OMC) was established to simulate space-based illumination conditions using equipment and techniques that recreate telescopic observations, particularly source-target-sensor orientations. The intent was to recreate light curves using known aspect angles of known targets and phase angles (angle is defined by the vertex between illumination source-object-detector) to complement telescopic observations that could be used to update the current optical size estimation model (OSEM) – a model that converts object brightness into size for orbital debris models. To support the above goals, the laboratory has undergone several equipment upgrades to increase capabilities over almost 20 years of operation. The primary instrumentation acquires reflectance measurements and includes a solar-like light source, CCD camera with astrometric filters, and robotic arm. A rotary arm was added approximately five years after full operation to allow acquisition through a full 360° range of phase angles. Another part of the OMC instrumentation is a field spectrometer, predominately used for field operations to acquire pre- and post-flight spacecraft material spectral measurements. Additionally, reflectance spectroscopy of various materials is also of interest resulting from hypervelocity impact tests, pristine spacecraft materials, or samples of materials that are used in spacecraft design. These measurements are stored in NASA’s Spectral Material Database, a resource that is still being populated today. The study of spectral measurements also enabled the development of spectral unmixing routines to support the identification of spacecraft materials from spectral data gathered by ground based telescopes. Preliminary OMC investigations focused on feasibility studies to acquire 360° rotation light curves of simple shapes at a single-phase angle and extended to measurements of representative fragments from ground-based explosion tests. To correlate the light curves with ground-based optical measurements, a focused study on high area to mass materials was conducted in support of a newly identified population (at the time) in geosynchronous orbit (GEO) consisting of multi-layered insulation. To further characterize orbital debris, a larger selection of materials was analyzed using laboratory photometric measurements that included representative targets from pristine spacecraft materials and ground-based impact tests. Around 2012, an initiative was requested to understand the feasibility of active debris removal (ADR) of larger targets using grappling methods for spent rocket bodies. Using a priori information on selected targets, scaled-down versions of rocket bodies were generated thanks to improvements in 3D printing technology and machining. These targets were studied in the OMC to understand rotation characteristics. These were compared with telescopic data to determine if the tumble and rotation angles would allow ADR. In 2013, the OMC focused on combining spectral measurements with photometric data to characterize GEO orbital debris. Several years later, NASA acquired a Titan III Transtage test article from “The Boneyard” with a high-resemblance to on-orbit Titan III Transtage rocket bodies, allowing physical access to a representative rocket body that suffered fragmentations in GEO. This prompted the creation of 3D models using lidar technology and spectral measurements of the materials. Focused research also transitioned to specific materials (i.e., solar cells) when telescopic surveys requested characterization of specific GEO targets. In the different research products presented, the focus has been to understand the various parameters that influence optical size estimation, including albedo, phase functions, and brightness variations. Work in this area continues with newer sources of data, including DebriSat, a high-fidelity 56-kg spacecraft replica representative of a modern low Earth orbit (LEO) satellite subjected to a laboratory hypervelocity impact test to understand fragmentation events and to support updates to satellite breakup models and size estimation models. Utilizing the vast population of fragments from DebriSat and prior laboratory impact experiments, the ODPO has focused on acquiring bidirectional reflectance distribution function (BRDF) data to characterize targets in the laboratory, thus removing aspect angle dependencies. Additionally, the DebriSat project has provided improved processes for measuring size via image acquisition, such that a true fragment size can be directly compared to the derived size using the OSEM. The team continues to assess BRDFs and use spectral measurement data to investigate the parameters used in the OSEM, specifically magnitudes, albedo, and phase functions.

Heather Cowardin↗

Dynamic model with scale-dependent coefficients in the viscous range

The standard dynamic procedure is based on the scale-invariance assumption that the model coefficient C is the same at the grid and test-filter levels. In many applications this condition is not met, e.g. when the filter-length, delta, approaches the Kolmogorov scale, and C(delta approaches eta) approaches O. Using a priori tests, we show that the standard dynamic model yields the coefficient corresponding to the test-filter scale (alpha delta) instead of the grid-scale (delta). Several approaches to account for scale dependence are examined and/or tested in large eddy simulation of isotropic turbulence: (a) take the limit alpha approaches 1; (b) solve for two unknown coefficients C(Delta) and C(alpha delta) in the least-square-error formulation; (c) the 'bi-dynamic model', in which two test-filters (e.g. at scales 2(delta) and 4(delta) are employed to gain additional information on possible scale-dependence of the coefficient, and an improved estimate for the grid-level coefficient is obtained by extrapolation, (d) use theoretical predictions for the ratio C(alpha delta)/C(delta) and dynamically solve for C(delta). None of these options is found to be entirely satisfactory, although the last approach appears applicable to the viscous range.

Meneveau, C.↗

Digitally Calibrated TR Modules Enabling Real-Time Beamforming SweepSAR Architectures

SweepSAR, a novel radar architecture that depends on a DBF (digital beamforming) array, requires calibration accuracies that are order(s) of magnitude greater than is possible with traditional techniques, such as a priori characterization of TR (transmit/receive) modules in thermal vacuum chambers, or simple loop-back of the calibration signal. The advantages of a SweepSAR architecture are so great that it is worth applying significant resources to calibration efforts. Due to the nature of the DBF, each channel contains a digitizer and very powerful digital processor. Each channel can independently digitize (with the digitizer) and analyze (with the processor) its channel's unique calibration signal, and extract the relevant calibration parameters, namely channel gain and channel phase delay commonly referred to as the gain (or amplitude) and phase of the channel. Using the processor, each channel's gain and phase can theoretically be estimated with arbitrary precision through averaging a sufficiently large number of samples. Systematic errors and the changing gain and phase of the channels, typically due to temperature drifts, limits how long the averaging can occur, which limits the precision of the calibration estimate. However, results indicate that calibration knowledge of both the transmit and receive chains of each TR module can be improved by one or two orders of magnitude. Due to the digital nature of the receiver data, the channel's gain and phase may be corrected by a similar amount, while the transmit chain can only be corrected in a traditional manner. To implement Sweep SAR, the order of magnitude improvement in the knowledge of the channel's gain and phase is needed, and the control of the receiver to a similar level is required. Inherent to the DBF array is the individual digitization of each of the array's receiver channels. Current systems typically combine all of the analog signals in the array into one or two analog channels, which are then digitized and processed. All signal conditioning performed prior to digitization is done using analog hardware (which is less precise than digital signal conditioning and dependent on temperature). The DBF digitizes every signal prior to combining, and can therefore analyze and correct received signals, as well as analyze signals that are being transmitted through analog hardware (by sampling a copy and digitizing). Each channel of a DBF also has a powerful processor. With this combination, one is able to digitize, analyze, and correct each channel prior to its being combined. A unique factor is the ability to digitize and analyze (in real time) each of the array's channels independently, allowing one to achieve unprecedented knowledge of each channel's performance (gain and phase), and since the combining is done digitally, each receive channel can be corrected prior to combining. This enables an unprecedented level of accuracy and control through onboard processing. SweepSAR promises significant increases in instrument capability for solid earth and biomass remote sensing, while reducing mission mass and cost. This new instrument concept requires new methods for calibrating the multiple channels, which must be combined onboard, in real time. New methods are being developed for digitally calibrating digital beam-forming arrays to reduce development time, risk, and cost of precision calibrated TR modules for array architectures by accurately tracking modules' characteristics through closed-loop digital calibration, thus tracking systematic changes regardless of temperature.-

Hoffman, James P.↗

Ozone vertical distribution retrieval from ground-based high resolution infrared solar spectra

A practical procedure for the retrieval of ozone vertical profiles from ground-based high resolution Fourier transform infrared solar spectra has been developed. The analysis is based on a multilayer line-by-line forward model and a semi-empirical version of the optimal estimation inversion method of Rodgers. The 1002.6-1003.2 cm(exp -1) spectral interval has been selected for the analysis on the basis of synthetic spectrum calculations. This interval contains numerous ozone lines covering a range of intensities and providing retrieval sensitivity from ground level to about 35 km. Characterization of the method and an error analysis have been performed. For a spectral resolution of 0.05-0.01 cm(exp -1) and a signal-to-noise ratio greater than or equal to 100 the retrieval is stable with a vertical resolution of approximately 5 km attainable near the surface degrading to approximately 10 km in the stratosphere. Synthetic spectra studies show that the a priori profile and weak constraints selected for the retrievals introduce no significant biases for a wide range of ozone profiles.

Pougatchev, N. S.↗

Accurate Predictions of Mean Geomagnetic Dipole Excursion and Reversal Frequencies, Mean Paleomagnetic Field Intensity, and the Radius of Earth's Core Using McLeod's Rule

The geomagnetic spatial power spectrum R(sub n)(r) is the mean square magnetic induction represented by degree n spherical harmonic coefficients of the internal scalar potential averaged over the geocentric sphere of radius r. McLeod's Rule for the magnetic field generated by Earth's core geodynamo says that the expected core surface power spectrum (R(sub nc)(c)) is inversely proportional to (2n + 1) for 1 less than n less than or equal to N(sub E). McLeod's Rule is verified by locating Earth's core with main field models of Magsat data; the estimated core radius of 3485 kn is close to the seismologic value for c of 3480 km. McLeod's Rule and similar forms are then calibrated with the model values of R(sub n) for 3 less than or = n less than or = 12. Extrapolation to the degree 1 dipole predicts the expectation value of Earth's dipole moment to be about 5.89 x 10(exp 22) Am(exp 2)rms (74.5% of the 1980 value) and the expected geomagnetic intensity to be about 35.6 (mu)T rms at Earth's surface. Archeo- and paleomagnetic field intensity data show these and related predictions to be reasonably accurate. The probability distribution chi(exp 2) with 2n+1 degrees of freedom is assigned to (2n + 1)R(sub nc)/(R(sub nc). Extending this to the dipole implies that an exceptionally weak absolute dipole moment (less than or = 20% of the 1980 value) will exist during 2.5% of geologic time. The mean duration for such major geomagnetic dipole power excursions, one quarter of which feature durable axial dipole reversal, is estimated from the modern dipole power time-scale and the statistical model of excursions. The resulting mean excursion duration of 2767 years forces us to predict an average of 9.04 excursions per million years, 2.26 axial dipole reversals per million years, and a mean reversal duration of 5533 years. Paleomagnetic data show these predictions to be quite accurate. McLeod's Rule led to accurate predictions of Earth's core radius, mean paleomagnetic field intensity, and mean geomagnetic dipole power excursion and axial dipole reversal frequencies. We conclude that McLeod's Rule helps unify geo-paleomagnetism, correctly relates theoretically predictable statistical properties of the core geodynamo to magnetic observation, and provides a priori information required for stochastic inversion of paleo-, archeo-, and/or historical geomagnetic measurements.

Voorhies, Coerte V.↗

Turbulent Output-Based Anisotropic Adaptation

Controlling discretization error is a remaining challenge for computational fluid dynamics simulation. Grid adaptation is applied to reduce estimated discretization error in drag or pressure integral output functions. To enable application to high O(10(exp 7)) Reynolds number turbulent flows, a hybrid approach is utilized that freezes the near-wall boundary layer grids and adapts the grid away from the no slip boundaries. The hybrid approach is not applicable to problems with under resolved initial boundary layer grids, but is a powerful technique for problems with important off-body anisotropic features. Supersonic nozzle plume, turbulent flat plate, and shock-boundary layer interaction examples are presented with comparisons to experimental measurements of pressure and velocity. Adapted grids are produced that resolve off-body features in locations that are not known a priori.

Park, Michael A.↗

Isopropanol dehydration reaction rate kinetics measurement using H 2 O time histories

H 2 O formation during thermal decomposition of isopropanol was measured behind reflected shock waves at temperatures ranging from 1127 to 1621 K at an average pressure of 1.42 atm using a laser absorption technique. Of the five modern chemical kinetics models used to compare the H 2 O time histories, the model from Li et al (Combust. Flame 2019;207:171-185) showed the best overall agreement. Sensitivity and rate of production analyses using the Li et al model (as well as those from AramcoMech 3.0, CRECK, and Togbe et al (Energy Fuel. 2011;25:676-683)) showed unimolecular dehydration of isopropanol, iC 3 H 7 OH ⇌ H 2 O + C 3 H 6 (R1), is nearly the sole reaction controlling H2O production at early times, allowing for an a priori measurement of the forward rate constant k 1 . The Arrhenius expression k1 (s –1 ) = 2.60 × 10 13 exp(-31 120 K/T) was determined to represent best the data from this study. According to the models and previous experimental investigations, the pressure investigated is well within the high-pressure limit (HPL) for this reaction. Additional, higher-pressure experiments also confirmed the HPL assumption. An uncertainty analysis was performed by varying secondary reactions within their uncertainties and examining their effect on the overall prediction, establishing an uncertainty within ±20% for all but the highest temperature cases, which have a maximum uncertainty of ±40%. Experiments conducted with a radical trapper, toluene, showed little influence from radical chemistry, suggesting this estimated uncertainty is fairly conservative. Experimental data from Heyne et al (Z Phys Chem. 2015;229:881-907) were found to be in good agreement with the rate measurements from this study and, therefore, a second Arrhenius expression, k 1 (s –1 ) = 2.11 × 10 13 exp(-30 820 K/T), was found to represent both datasets well. This second expression has a larger temperature range of 976-1621 K. Here the present study provides the first high-temperature data collected for this reaction, adding to the limited data available for isopropanol in the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Earth observing scanning polarimeter

Climate forcing by tropospheric aerosols is receiving increased attention because of the realization that the climate effects may be large, while our knowledge of global aerosol characteristics and temporal changes is very poor. Tropospheric aerosols cause a direct radiative forcing due simply to their scattering and absorption of solar radiation, as well as an indirect effect as cloud condensation nuclei which can modify the shortwave reflectivity of clouds. Sulfate aerosols tend to increase planetary albedo through both the direct and indirect effects; a cooling due to anthropogenic sulfate aerosols has been estimated of order 1 W/sq m, noting that this is similar in magnitude to the present anthropogenic greenhouse gas warming. Other aerosols, including those from biomass burning and wind-blown desert dust are also of potential climatic importance. At present, the only global monitoring of tropospheric aerosols is a NOAA operational product, aerosol optical thickness, obtained using channel-1 (0.58-0.68 mu m) radiances from the AVHRR. With this single channel radiance data, one must use an approach which is based on the inferred excess of reflected radiance owing to scattering by the aerosols over that expected from theoretical calculations. This approach is suited only for situations where the surface has a low albedo that is well known a priori. Thus, the NOAA operational product is restricted to coverage over the ocean at AVHRR scan angles well away from sun glint, and aerosol changes are subject to confusion with changes caused by either optically thin or subpixel clouds. Because optically thin aerosols have only a small effect on the radiance, accurate measurements for optical thickness less than 0.1 (which is a typical background level) are precluded. Moreover, some of the largest and most important aerosol changes are expected over land. The Earth Observing Scanning Polarimeter (EOSP) instrument, based upon design heritage and analysis techniques developed for planetary missions, will retrieve tropospheric aerosol characteristics from measurements of multispectral radiance and polarization. Moreover, the same radiance and polarization measurements will also provide very precise information on cloud properties and maps of surface characteristics for cloud-free regions. These capabilities also give EOSP the unique ability to discriminate aerosol from clouds and surface.

Travis, Larry↗

Modeling of LEO Orbital Debris Populations in Centimeter and Millimeter Size Regimes

The building of the NASA Orbital Debris Engineering Model, whether ORDEM2000 or its recently updated version ORDEM2010, uses as its foundation a number of model debris populations, each truncated at a minimum object-size ranging from 10 micron to 1 m. This paper discusses the development of the ORDEM2010 model debris populations in LEO (low Earth orbit), focusing on centimeter (smaller than 10 cm) and millimeter size regimes. Primary data sets used in the statistical derivation of the cm- and mm-size model populations are from the Haystack radar operated in a staring mode. Unlike cataloged objects of sizes greater than approximately 10 cm, ground-based radars monitor smaller-size debris only in a statistical manner instead of tracking every piece. The mono-static Haystack radar can detect debris as small as approximately 5 mm at moderate LEO altitudes. Estimation of millimeter debris populations (for objects smaller than approximately 6 mm) rests largely on Goldstone radar measurements. The bi-static Goldstone radar can detect 2- to 3-mm objects. The modeling of the cm- and mm-debris populations follows the general approach to developing other ORDEM2010-required model populations for various components and types of debris. It relies on appropriate reference populations to provide necessary prior information on the orbital structures and other important characteristics of the debris objects. NASA's LEO-to-GEO Environment Debris (LEGEND) model is capable of furnishing such reference populations in the desired size range. A Bayesian statistical inference process, commonly adopted in ORDEM2010 model-population derivations, changes a priori distribution into a posteriori distribution and thus refines the reference populations in terms of data. This paper describes key elements and major steps in the statistical derivations of the cm- and mm-size debris populations and presents results. Due to lack of data for near 1-mm sizes, the model populations of 1- to 3.16-mm objects are an empirical extension from larger debris. The extension takes into account the results of micro-debris (from 10 micron to 1 mm) population modeling that is based on shuttle impact data, in the hope of making a smooth transition between micron and millimeter size regimes. This paper also includes a brief discussion on issues and potential future work concerning the analysis and interpretation of Goldstone radar data.

Xu, Y.-L.↗

Design of partially supervised classifiers for multispectral image data

A partially supervised classification problem is addressed, especially when the class definition and corresponding training samples are provided a priori only for just one particular class. In practical applications of pattern classification techniques, a frequently observed characteristic is the heavy, often nearly impossible requirements on representative prior statistical class characteristics of all classes in a given data set. Considering the effort in both time and man-power required to have a well-defined, exhaustive list of classes with a corresponding representative set of training samples, this 'partially' supervised capability would be very desirable, assuming adequate classifier performance can be obtained. Two different classification algorithms are developed to achieve simplicity in classifier design by reducing the requirement of prior statistical information without sacrificing significant classifying capability. The first one is based on optimal significance testing, where the optimal acceptance probability is estimated directly from the data set. In the second approach, the partially supervised classification is considered as a problem of unsupervised clustering with initially one known cluster or class. A weighted unsupervised clustering procedure is developed to automatically define other classes and estimate their class statistics. The operational simplicity thus realized should make these partially supervised classification schemes very viable tools in pattern classification.

Jeon, Byeungwoo↗

Adaptive resource allocation for surrogate modeling of systems comprised of multiple disciplines with varying fidelity

We present an adaptive algorithm for constructing surrogate models for integrated systems composed of a set of coupled components. With this goal we introduce ‘coupling’ variables with a priori unknown distributions that allow approximations of each component to be built independently. Once built, the surrogates of the components are combined and used to predict system-level quantities of interest (QoI) at a fraction of the cost of interrogating the full system model. We use a greedy experimental design procedure, based upon a modification of Multi-Index Stochastic Collocation (MISC), to minimize the error of the combined surrogate. This is achieved by refining each component surrogate in accordance with its relative contribution to error in the approximation of the system-level QoI. Our adaptation of MISC is a multi-fidelity procedure that can leverage ensembles of models of varying cost and accuracy, for one or more components, to produce estimates of system-level QoI. Several numerical examples demonstrate the efficacy of the proposed approach on systems involving feed-forward and feedback coupling. For a fixed computational budget, the proposed algorithm is able to produce approximations that are orders of magnitude more accurate than approximations that treat the integrated system as a black-box.

97 MATHEMATICS AND COMPUTING↗

Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated nitrogen atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. Furthermore, these results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Representation of Probability Density Functions from Orbit Determination using the Particle Filter

Statistical orbit determination enables us to obtain estimates of the state and the statistical information of its region of uncertainty. In order to obtain an accurate representation of the probability density function (PDF) that incorporates higher order statistical information, we propose the use of nonlinear estimation methods such as the Particle Filter. The Particle Filter (PF) is capable of providing a PDF representation of the state estimates whose accuracy is dependent on the number of particles or samples used. For this method to be applicable to real case scenarios, we need a way of accurately representing the PDF in a compressed manner with little information loss. Hence we propose using the Independent Component Analysis (ICA) as a non-Gaussian dimensional reduction method that is capable of maintaining higher order statistical information obtained using the PF. Methods such as the Principal Component Analysis (PCA) are based on utilizing up to second order statistics, hence will not suffice in maintaining maximum information content. Both the PCA and the ICA are applied to two scenarios that involve a highly eccentric orbit with a lower apriori uncertainty covariance and a less eccentric orbit with a higher a priori uncertainty covariance, to illustrate the capability of the ICA in relation to the PCA.

Mashiku, Alinda K.↗