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DOE OSTI2023

Non-asymptotic analysis of ensemble Kalman updates: effective dimension and localization

Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in applications where generating each particle is costly. This paper develops a non-asymptotic analysis of ensemble Kalman updates, which rigorously explains why a small ensemble size suffices if the prior covariance has moderate effective dimension due to fast spectrum decay or approximate sparsity. Here, we present our theory in a unified framework, comparing everal implementations of ensemble Kalman updates that use perturbed observations, square root filtering and localization. As part of our analysis, we develop new dimension-free covariance estimation bounds for approximately sparse matrices that may be of independent interest.

Mathematics↗

NASA NTRS1994

Polarimetric method of estimation of vertical aerosol distribution in application to observations of ozone and NO2

The degree of polarization of skylight at the zenith during twilight depends on the aerosol content in the atmosphere. The long-term observations at the high-mountain research station 'Kislovodsk' (North Caucasus) have shown that the variation of the degree of polarization after the eruption of the El Chichon volcano can serve as the effective parameter characterizing the vertical aerosol stratification in the atmosphere. The results of the measurements are confirmed by the numerical calculations. The algorithm of the retrieval of the vertical aerosol distribution on the base of the measurements of the degree of polarization is proposed. This method can be applied for the increasing of the precision of O3, NO2, and other gas content measurements.

Elansky, Nikolay F.↗

DOE OSTI2015

Microwave and millimeter wave dielectric permittivity and magnetic permeability of epsilon-gallium-iron-oxide nano-powders

In millimeter wave frequency range, hexagonal ferrites with high uniaxial anisotropic magnetic fields are used as absorbers. These ferrites include M-type barium ferrite (BaFe{sub 12}O{sub 19}) and strontium ferrite (SrFe{sub 12}O{sub 19}), which have natural ferromagnetic resonant frequency range from 40 GHz to 60 GHz. However, the higher frequency range lacks suitable materials that support the higher frequency ferromagnetic resonance. A series of gallium-substituted ε-iron oxides (ε-Ga{sub x}Fe{sub 2−x}O{sub 3}) are synthesized, which have ferromagnetic resonant frequencies appearing over the frequency range of 30 GHz to 150 GHz. The ε-Ga{sub x}Fe{sub 2−x}O{sub 3} is synthesized by the sol-gel method. The particle sizes are observed to be smaller than 100 nm. In this paper, in-waveguide transmission and reflection method and the free space magneto-optical approach have been employed to study these newly developed ε-Ga{sub x}Fe{sub 2−x}O{sub 3} particles in millimeter waves. These techniques enable to obtain precise transmission spectra to determine the dielectric and magnetic properties of both isotropic and anisotropic ferrites in the microwave and millimeter wave frequency range from single set of direct measurements. The complex dielectric permittivity and magnetic permeability spectra of ε-Ga{sub x}Fe{sub 2−x}O{sub 3} are shown in this paper. Strong ferromagnetic resonances at different frequencies determined by the x parameter are found.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1972

An engineering optimization method with application to STOL-aircraft approach and landing trajectories

An optimization method has been developed that computes the optimal open loop inputs for a dynamical system by observing only its output. The method reduces to static optimization by expressing the inputs as series of functions with parameters to be optimized. Since the method is not concerned with the details of the dynamical system to be optimized, it works for both linear and nonlinear systems. The method and the application to optimizing longitudinal landing paths for a STOL aircraft with an augmented wing are discussed. Noise, fuel, time, and path deviation minimizations are considered with and without angle of attack, acceleration excursion, flight path, endpoint, and other constraints.

Jacob, H. G.↗

NASA NTRS1986

Satellite scatterometer comparisons with surface measurements: Techniques and Seasat results

A method by which satellite and surface measurements can be compared in order to validate satellite wind observations is presented. The regression method requires knowledge of the expected differences (due to atmospheric variability and differing averaging) between perfect satellite and perfect buoy measurements. A model for estimating these differences is described. The regression method is applied to comparisons between Seasat Scatterometer (SASS) and U.S. National Data Buoy Office buoy data. Comparisons indicating a dependence of SASS accuracy on sea-surface temperature are summarized.

Freilich, Michael H.↗

NASA NTRS1991

Rainfall estimation over oceans from scanning multichannel microwave radiometer and special sensor microwave/imager microwave data

The brightness temperature (T sub b) measured at 37 GHz shows fairly strong emission from rain, and only slight effects caused by scattering by ice above the rain clouds. At frequencies below 37 GHz, were the fov is larger and the volume extinction coefficient is weaker, it is found that the observations do not yield appreciable additional information about rain. At 85 GHz (fov = 15 km), where the volume extinction is considerably larger, direct information about rain below the clouds is usually masked. Based on the above ideas, 37 GHz observations with a 30 km fov from SMMR and SSM/I are selected to develop an empirical method for the estimation of rain rate. In this method, the statistics of the observed T sub b's at 37 GHz in a rain storm are related to the rain rate statistics in that storm. The underestimation of rain rate, arising from the inability of the radiometer to respond sensitively to rain rate above a given threshold, is rectified in this technique with the aid of two parameters that depend on the total water vapor content in the atmosphere. The retrieved rain rates compare favorably with radar observations and monthly mean global maps of rain derived from this technique over the oceans.

Prabhakara, C.↗

NASA NTRS1992

Rainfall estimation over oceans from SMMR and SSM/I microwave data

The brightness temperature (T sub b) measured at 37 GHz shows fairly strong emission from rain, and only slight effects caused by scattering by ice above the rain clouds. At frequencies below 37 GHz, where the FOV is larger and the volume extinction coefficient is weaker, it is found that the observations do not yield appreciable additional information about rain. At 85 GHz (FOV = 15 km), where the volume extinction is considerably larger, direct information about rain below the clouds is usually masked. Based on the above idea, 37 GHz observations with a 30 km FOV from SMMR and SSM/I are selected to develop an empirical method for the estimation of rain rate. In this method, the statistics of the observed T sub b's at 37 GHz in a rain storm are related to the rain rate statistics in that storm. The underestimation of rain rate, arising from the inability of the radiometer to respond sensitively to rain rate above a given threshold is rectified in this technique with the aid of two parameters that depend on the total water vapor content in the atmosphere. The retrieved rain rates compare favorably with radar observations and monthly mean global maps of rain derived from this technique over the oceans.

Prabhakara, C.↗

NASA NTRS1994

Is a data set distributed as a power law? A test, with application to gamma-ray burst brightnesses

We present a method to determine whether an observed sample of data is drawn from a parent distribution that is pure power law. The method starts from a class of statistics which have zero expectation value under the null hypothesis, H(sub 0), that the distribution is a pure power law: F(x) varies as x(exp -alpha). We study one simple member of the class, named the `bending statistic' B, in detail. It is most effective for detection a type of deviation from a power law where the power-law slope varies slowly and monotonically as a function of x. Our estimator of B has a distribution under H(sub 0) that depends only on the size of the sample, not on the parameters of the parent population, and is approximated well by a normal distribution even for modest sample sizes. The bending statistic can therefore be used to test a set of numbers is drawn from any power-law parent population. Since many measurable quantities in astrophysics have distriibutions that are approximately power laws, and since deviations from the ideal power law often provide interesting information about the object of study (e.g., a `bend' or `break' in a luminosity function, a line in an X- or gamma-ray spectrum), we believe that a test of this type will be useful in many different contexts. In the present paper, we apply our test to various subsamples of gamma-ray burst brightness from the first-year Burst and Transient Source Experiment (BATSE) catalog and show that we can only marginally detect the expected steepening of the log (N (greater than C(sub max))) - log (C(sub max)) distribution.

Wijers, Ralph A. M. J.↗

DOE OSTI2025

147 Nd Quantification Using HSCCC-Purified Samples

Quantifying the fission product 147 Nd in nuclear debris samples is an important component of post-detonation nuclear forensics. The most accurate quantifications are obtained when Nd is purified from all other fission products, actinides, activation products, and environmental matrix contained within the debris. In this study, a recently developed method for Nd purification was tested, purifying 147 Nd from solutions of mixed fission products using high-speed counter-current chromatography (HSCCC). Importantly, the new method allowed for faster elution of Nd from the column as compared with established high performance liquid chromatography (HPLC) methods, and resulted in accurate/precise 147 Nd quantification by gamma-ray spectrometry. While the up-front equipment costs associated with HSCCC may be higher, its operational costs are on par with those of HPLC (solvents, extractants, power). Gas-flow proportional beta decay counting revealed contamination from the nearest neighbor lanthanide 143 Pr (a gamma-silent radioisotope) in the HSCCC-purified samples, but the activity contribution from 147 Nd could still be quantified. Remarkably consistent elution profiles were observed for the HSCCC method, spanning rare earth element (REE) loadings of more than 10 orders of magnitude (tracer to mmol quantities). In conclusion, the reliability and speed of the new method suggest utility for the rapid separation and quantification of 147 Nd in unknown samples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1978

A comparison of the noise produced by a small jet on a moving vehicle with that in a free jet

A 2.54 cm (1.00 in.) nozzle supplied with nitrogen was mounted above an automobile and driven over an asphalt roadway past stationary microphones in an attempt to quantify the effects of the vehicle motion on jet mixing noise. The nozzle was then tested in the Langley anechoic noise facility with a large free jet simulating the relative motion. The results are compared for these two methods of investigating forward speed effects on jet mixing noise. The vehicle results indicate a noise with forward speed throughout the Doppler-shifted static spectrum. This decrease across the entire frequency range was also apparent in the free-jet results. The similarity of the results indicates that the effects of flight on jet mixing noise can be predicted by simulation of forward speed with a free jet. Overall sound pressure levels were found to decrease with forward speed at all observation angles for both methods of testing.

Norum, T. D.↗

NASA NTRS2018

Observations of Fast-Moving Features in the Debris Disk of AU Mic on a Three-Year Timescale: Confirmation and New Discoveries

Context. The nearby and young M star AU Mic is surrounded by a debris disk in which we previously identified a series of large-scale arch-like structures that have never been seen before in any other debris disk and that move outward at high velocities. Aims. We initiated a monitoring program with the following objectives: (1) track the location of the structures and better constrain their projected speeds, (2) search for new features emerging closer in, and ultimately (3) understand the mechanism responsible for the motion and production of the disk features. Methods. AU Mic was observed at 11 different epochs between August 2014 and October 2017 with the IR camera and spectrograph of SPHERE. These high-contrast imaging data were processed with a variety of angular, spectral, and polarimetric differential imaging techniques to reveal the faintest structures in the disk. We measured the projected separations of the features in a systematic way for all epochs. We also applied the very same measurements to older observations from the Hubble Space Telescope (HST) with the visible cameras STIS and ACS. Results. The main outcomes of this work are (1) the recovery of the five southeastern broad arch-like structures we identified in our first study, and confirmation of their fast motion (projected speed in the range 4–12 km/s); (2) the confirmation that the very first structures observed in 2004 with ACS are indeed connected to those observed later with STIS and now SPHERE; (3) the discovery of two new very compact structures at the northwest side of the disk (at 0.40′′ and 0.55′′ in May 2015) that move to the southeast at low speed; and (4) the identification of a new arch-like structure that might be emerging at the southeast side at about 0.4′′ from the star (as of May 2016). Conclusions. Although the exquisite sensitivity of SPHERE allows one to follow the evolution not only of the projected separation, but also of the specific morphology of each individual feature, it remains difficult to distinguish between possible dynamical scenarios that may explain the observations. Understanding the exact origin of these features, the way they are generated, and their evolution over time is certainly a significant challenge in the context of planetary system formation around M stars.

Boccaletti, A.↗

DOE OSTI2022

An objective inter-comparison of trash mark constellations generated by manual and automated detection methods

Trash marks are unintentional markings observed on printed, scanned, or photocopied documents that result from permanent defects or transient material in office machines and can be used for source attribution of questioned documents. Trash mark examinations have been in use in forensic laboratories for decades, yet the method remains relatively untested and relies on training, experience, and anecdotal information to support its validity. Herein this study generated and harnessed objective data to empirically test one of the foundational theories for assessing the origin of photocopied documents: provided trash marks are present in sufficient quantity and/or quality, no two machines will exhibit a constellation of trash marks that is indistinguishable from another. In this project, objective trash mark location and size data was generated for 50 known photocopiers using both a traditional and a novel, automated method. Inter-machine comparisons were conducted using a novel variant of the Hausdorff distance algorithm to generate a quantitative assessment of how similar or different the 2450 pairs of trash mark constellations were from one another. This study found that each of the machines bearing one or more trash marks exhibited objective differences in their trash mark constellations, ultimately providing support for the tested hypothesis

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2007

On the Determination of Poisson Statistics for Haystack Radar Observations of Orbital Debris

A convenient and powerful method is used to determine if radar detections of orbital debris are observed according to Poisson statistics. This is done by analyzing the time interval between detection events. For Poisson statistics, the probability distribution of the time interval between events is shown to be an exponential distribution. This distribution is a special case of the Erlang distribution that is used in estimating traffic loads on telecommunication networks. Poisson statistics form the basis of many orbital debris models but the statistical basis of these models has not been clearly demonstrated empirically until now. Interestingly, during the fiscal year 2003 observations with the Haystack radar in a fixed staring mode, there are no statistically significant deviations observed from that expected with Poisson statistics, either independent or dependent of altitude or inclination. One would potentially expect some significant clustering of events in time as a result of satellite breakups, but the presence of Poisson statistics indicates that such debris disperse rapidly with respect to Haystack's very narrow radar beam. An exception to Poisson statistics is observed in the months following the intentional breakup of the Fengyun satellite in January 2007.

Stokely, Christopher L.↗

NASA NTRS1992

Development of a four-dimensional variational analysis system using the adjoint method at GLA. I - Dynamics

Recent developments in the field of data assimilation have pointed to variational analysis (essentially least-squares fitting of a model solution to observed data) using the adjoint method as a new direction that holds the potential of major improvements over the current optimal interpolation method. This paper describes the initial effort in the development of a 4D variational analysis system. Although the development is based on the Goddard Laboratory for Atmospheres General Circulation Model (GCM), the methods and procedures described in this paper can be applied to any model. The adjoint code that computes the gradients needed in the analysis can be written directly from the GCM code. An easy error-detection technique was devised in the construction of the adjoint model. Also, a method of determining the weights and the preconditioning scales for the cases where model-generated data, which are error free, are used as observation is proposed. Two test experiments show that the dynamics part of the system has been successfully completed.

Chao, Winston C.↗

DOE OSTI2016

PROBING THE EXPANSION HISTORY OF THE UNIVERSE BY MODEL-INDEPENDENT RECONSTRUCTION FROM SUPERNOVAE AND GAMMA-RAY BURST MEASUREMENTS

To probe the late evolution history of the universe, we adopt two kinds of optimal basis systems. One of them is constructed by performing the principle component analysis, and the other is built by taking the multidimensional scaling approach. Cosmological observables such as the luminosity distance can be decomposed into these basis systems. These basis systems are optimized for different kinds of cosmological models that are based on different physical assumptions, even for a mixture model of them. Therefore, the so-called feature space that is projected from the basis systems is cosmological model independent, and it provides a parameterization for studying and reconstructing the Hubble expansion rate from the supernova luminosity distance and even gamma-ray burst (GRB) data with self-calibration. The circular problem when using GRBs as cosmological candles is naturally eliminated in this procedure. By using the Levenberg–Marquardt technique and the Markov Chain Monte Carlo method, we perform an observational constraint on this kind of parameterization. The data we used include the “joint light-curve analysis” data set that consists of 740 Type Ia supernovae and 109 long GRBs with the well-known Amati relation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

A Cohesive Deep Drilling Field Strategy for LSST Cosmology

The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will image billions of astronomical objects in the wide–fast–deep primary survey and in a set of minisurveys including intensive observations of a group of deep drilling fields (DDFs). The DDFs are a critical piece of three key aspects of the LSST Dark Energy Science Collaboration (DESC) cosmological measurements: they provide a required calibration for photometric redshifts (photo- z ) and weak gravitational lensing (WL) measurements and they directly contribute to cosmological constraints from the most distant Type Ia supernovae (SNe Ia). We present a set of cohesive DDF strategies fulfilling science requirements relevant to DESC and following the guidelines of the Survey Cadence Optimization Committee. We propose a method to estimate the observing strategy parameters and we perform simulations of the corresponding surveys. We define a set of metrics for each science case to assess the performance of the proposed observing strategies. We show that the most promising results are achieved with deep rolling surveys characterized by two sets of fields: ultradeep fields ( z ≲ 1.1) observed at a high cadence with a large number of visits over a limited number of seasons, and deep fields ( z ≲ 0.7), observed with a cadence of ~3 nights for 10 yr. These encouraging results should be confirmed with realistic simulations using the LSST scheduler. A DDF budget of ~8.5% is required to design observing strategies satisfying all the cosmological requirements. A lower DDF budget leads to surveys that either do not fulfill the photo- z /WL requirements or are not optimal for SN Ia cosmology.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

A hybrid Monte Carlo, discontinuous Galerkin method for linear kinetic transport equations

Here we present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise constant solution and the discrete ordinates use bilinear discontinuous finite elements. From the hybridization of the problem, the resulting problem solved by Monte Carlo is scattering free, resulting in a simple, efficient solution procedure. Between time steps, we use a projection approach to “relabel” collided particles as uncollided particles. In conclusion, from a series of standard 2-D Cartesian test problems we observe that our hybrid method has improved accuracy and reduction in computational complexity of approximately an order of magnitude relative to standard discrete ordinates solutions.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2012

Launch Method for Kites in Low-Wind or No-Wind Conditions

Airborne observations using lightweight camera systems are desirable for a variety of applications. This system was contemplated as a method to provide a simple remote sensing aerial platform. Kites have been successfully employed for aerial observations, but have historically required natural wind or towing to become airborne. This new method negates this requirement, and widens the applicability of kites for carrying instrumentation. Applicability is primarily limited by the space available on the ground for launching. The innovation is a method for launching kites in low-wind or no-wind conditions. This method will enable instrumentation to be carried aloft using simple (or complex) kite-based systems, to obtain observations from an aerial perspective. This technique will provide access to altitudes of 100 meters or more over any area normally suited for kite flying. The duration of any observation is dependent on wind strength; however, the initial altitude is relatively independent. The system does not require any electrical or combustion-based elements. This technology was developed to augment local-scale airborne measurement capabilities suitable for Earth science research, agricultural productivity, and environmental observations. The method represents an extension of techniques often used in aeronautical applications for launching fixed-wing aircraft, such as sailplanes, using mechanical means not incorporated in the aircraft itself. The innovation consists of an elastic cord (for propulsive force), a tether extension (optional, for additional height), and the kite (instrumentation optional). Operation of the system is accomplished by fixing the elastic cord to ground (or equivalent), attaching the cord with/or without a tether extension to the kite, tensioning the system to store energy, and releasing the kite. The kite will climb until energy is dissipated.

Bland, Geoffrey↗