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NASA NTRS1994

Improvements to TOVS retrievals over sea ice and applications to estimating Arctic energy fluxes

Modeling studies suggest that polar regions play a major role in modulating the Earth's climate and that they may be more sensitive than lower latitudes to climate change. Until recently, however, data from meteorological stations poleward of 70 degs have been sparse, and consequently, our understanding of air-sea-ice interaction processes is relatively poor. Satellite-borne sensors now offer a promising opportunity to observe polar regions and ultimately to improve parameterizations of energy transfer processes in climate models. This study focuses on the application of the TIROS-N operational vertical sounder (TOVS) to sea-ice-covered regions in the nonmelt season. TOVS radiances are processed with the improved initialization inversion ('3I') algorithm, providng estimates of layer-average temperature and moisture, cloud conditions, and surface characteristics at a horizontal resolution of approximately 100 km x 100 km. Although TOVS has flown continuously on polar-orbiting satellites since 1978, its potential has not been realized in high latitudes because the quality of retrievals is often significantly lower over sea ice and snow than over the surfaces. The recent availability of three Arctic data sets has provided an opportunity to validate TOVS retrievals: the first from the Coordinated Eastern Arctic Experiment (CEAREX) in winter 1988/1989, the second from the LeadEx field program in spring 1992, and the third from Russian drifting ice stations. Comparisons with these data reveal deficiencies in TOVS retrievals over sea ice during the cold season; e.g., ice surface temperature is often 5 to 15 K too warm, microwave emissivity is approximately 15% too low at large view angles, clear/cloudy scenes are sometimes misidentified, and low-level inversions are often not captured. In this study, methods to reduce these errors are investigated. Improvements to the ice surface temperature retrieval have reduced rms errors from approximately 7 K to 3 K; correction of microwaves (50 GHz) brightness temperatures for view angle dependence now allows the surface type (open water versus sea ice) to be determined; modifications to the clear/cloud tests have improved cloud detection over sea ice, especially where it is inhomogeneous; and improved surface temperature estimates have resulted in more successful diagnoses of low-level stratification. Applications of improved retrievals to studies of the Arctic energy budget are encouraging. Preliminary calculations of air-ice stress vectors, 10-m wind speed, and horizontal advection of heat and moisture are presented.

Francis, Jennifer A.↗

NASA NTRS1994

Gradients in giant branch morphology in the core of 47 Tucanae

I describe an algorithm which uses the high spatial resolution of the Hubble Space Telescope to complement the high spatial-to-noise, approximately symmetric point response function, relatively large spatial coverage, and standard filters available from ground based images of crowded fields. Applying this technique to the central regions of the globular cluster 47 Tucanae, I find that the morphology of the giant branch in the core is significantly different from that in more distant regions (r approximately equals 5 to 10 core radii) of the cluster. In particular, there appear to be fewer bright giants in the core, along with an enhanced `asymptotic giant branch' (AGB) sequence. Depletion of giants has been observed in the cores of other dense clusters, and may be due to `stripping' of large stars by stellar encounters and/or mass transfer in binary systems. Central concentrations of true asymptotic giant branch stars are not expected to result from dynamical processes; possibly some of these stars may be evolved blue stragglers.

Bailyn, Charles D.↗

NASA NTRS1998

SPARCLE: Validation of Observing System Simulations (SPace Readiness Coherent Lidar Experiment)

NASA recently approved a mission to fly a Doppler Wind Lidar (DWL) on a U.S. Space Shuttle. SPARCLE, managed by Marshall Space Flight Center in Huntsville, AL, is targeted for launch in March 2001. This mission is viewed as a necessary demonstration of a solid state (2 micron) lidar using coherent detection before committing resources to a 3-5 year research or operational mission. While, to many, this shuttle mission is seen as the first step in a series leading to a fully operational wind observing system, to others, it is a chance to validate predictions of performance based upon theoretical models, analyses of airborne and ground-based data, and sophisticated observing system simulation experiments. This paper will be presented in two parts: first a brief overview of the SPARCLE mission and second, a summary of current performance predictions and key contributions from ground- based and airborne DWL research. The SPARCLE instrument is a 100 mJ, 6 Hz, diode-pumped 2-micron laser with a .25 m telescope using heterodyne mixing in a fiber and an InGaAs detector. A 25 cm silicon wedge scanner will be used in step-stare modes with dwells ranging from 60 seconds to .5 seconds. Pointing knowledge is achieved with a dedicated GPS/INS mounted close to the lidar. NASA's Hitchhiker program is providing the instrument enclosures (2 cans) and mission logistics support. An on-board data system is sized to record 150 Gbytes of raw signal from a two 400 MHZ A/D converters. On-board signal processing will be used to control the frequency of the Local Oscillator. SPARCLE is predicted to have a single shot backscatter sensitivity near 1x10(exp -6) m-1 sr-1, To achieve higher sensitivity, shot accumulation will be employed. Ground-based, 2 micron DWLs have been used to assess the benefits of shot accumulation (approximately SQRT for SNR). Airborne programs like MACAWS have provided good datasets for evaluating various sampling strategies and signal processing algorithms. Using these real data to calibrate our simulation models, we can describe when and how well SPARCLE is expected to preform. Outputs from these performance models will be presented.

Emmitt, G. D.↗

NASA NTRS2000

A Simple Tool for the Design and Analysis of Multiple-Reflector Antennas in a Multi-Disciplinary Environment

The process of designing and analyzing a multiple-reflector system has traditionally been time-intensive, requiring large amounts of both computational and human time. At many frequencies, a discrete approximation of the radiation integral may be used to model the system. The code which implements this physical optics (PO) algorithm was developed at the Jet Propulsion Laboratory. It analyzes systems of antennas in pairs, and for each pair, the analysis can be computationally time-consuming. Additionally, the antennas must be described using a local coordinate system for each antenna, which makes it difficult to integrate the design into a multi-disciplinary framework in which there is traditionally one global coordinate system, even before considering deforming the antenna as prescribed by external structural and/or thermal factors. Finally, setting up the code to correctly analyze all the antenna pairs in the system can take a fair amount of time, and introduces possible human error. The use of parallel computing to reduce the computational time required for the analysis of a given pair of antennas has been previously discussed. This paper focuses on the other problems mentioned above. It will present a methodology and examples of use of an automated tool that performs the analysis of a complete multiple-reflector system in an integrated multi-disciplinary environment (including CAD modeling, and structural and thermal analysis) at the click of a button. This tool, named MOD Tool (Millimeter-wave Optics Design Tool), has been designed and implemented as a distributed tool, with a client that runs almost identically on Unix, Mac, and Windows platforms, and a server that runs primarily on a Unix workstation and can interact with parallel supercomputers with simple instruction from the user interacting with the client.

Katz, Daniel S.↗

NASA NTRS2000

Validation of MODIS Aerosol Retrievals during PRIDE

The Puerto Rico Dust Experiment (PRIDE) was held in Roosevelt Roads, Puerto Rico from June 26 to July 24, 2000. It was intended to study the radiative and microphysical properties of Saharan dust transported into Puerto Rico. PRIDE had the unique distinction of being the first major field experiment to allow direct comparison of aerosol retrievals from MODIS (MODerate Imaging Spectro-radiometer - aboard the Terra satellite) with data from a variety of ground, shipboard and air-based instruments. Over the ocean the MODIS algorithm retrieves optical depth as well as information about the aerosol's size. During PRIDE, MODIS passed over Roosevelt Roads approximately once per day during daylight hours. Due to sunglint and clouds over Puerto Rico, aerosol retrievals can be made from only about half the MODIS scenes. In this study we try to "validate" our aerosol retrievals by comparing to measurements taken by sun-photometers from multiple platforms, including: Cimel (AERONET) from the ground, Microtops (handheld) from ground and ship, and the NASA-Ames sunphotometer from the air.

Levy, R.↗

NASA NTRS2003

Real-Time Attitude Independent Three Axis Magnetometer Calibration

In this paper new real-time approaches for three-axis magnetometer sensor calibration are derived. These approaches rely on a conversion of the magnetometer-body and geomagnetic-reference vectors into an attitude independent observation by using scalar checking. The goal of the full calibration problem involves the determination of the magnetometer bias vector, scale factors and non-orthogonality corrections. Although the actual solution to this full calibration problem involves the minimization of a quartic loss function, the problem can be converted into a quadratic loss function by a centering approximation. This leads to a simple batch linear least squares solution. In this paper we develop alternative real-time algorithms based on both the extended Kalman filter and Unscented filter. With these real-time algorithms, a full magnetometer calibration can now be performed on-orbit during typical spacecraft mission-mode operations. Simulation results indicate that both algorithms provide accurate integer resolution in real time, but the Unscented filter is more robust to large initial condition errors than the extended Kalman filter. The algorithms are also tested using actual data from the Transition Region and Coronal Explorer (TRACE).

Crassidis, John L.↗

NASA NTRS1999

A Simple Tool for the Design and Analysis of Multiple-reflector Antennas in a Multi-disciplinary Environment

Katz, Daniel, S.↗

NASA NTRS2007

Optimizations of a Hardware Decoder for Deep-Space Optical Communications

The National Aeronautics and Space Administration has developed a capacity approaching modulation and coding scheme that comprises a serial concatenation of an inner accumulate pulse-position modulation (PPM) and an outer convolutional code [or serially concatenated PPM (SCPPM)] for deep-space optical communications. Decoding of this code uses the turbo principle. However, due to the nonbinary property of SCPPM, a straightforward application of classical turbo decoding is very inefficient. Here, we present various optimizations applicable in hardware implementation of the SCPPM decoder. More specifically, we feature a Super Gamma computation to efficiently handle parallel trellis edges, a pipeline-friendly 'maxstar top-2' circuit that reduces the max-only approximation penalty, a low-latency cyclic redundancy check circuit for window-based decoders, and a high-speed algorithmic polynomial interleaver that leads to memory savings. Using the featured optimizations, we implement a 6.72 megabits-per-second (Mbps) SCPPM decoder on a single field-programmable gate array (FPGA). Compared to the current data rate of 256 kilobits per second from Mars, the SCPPM coded scheme represents a throughput increase of more than twenty-six fold. Extension to a 50-Mbps decoder on a board with multiple FPGAs follows naturally. We show through hardware simulations that the SCPPM coded system can operate within 1 dB of the Shannon capacity at nominal operating conditions.

quadratic polynomial interleaver↗

NASA NTRS2016

L-Band RFI in Japan

In recent years, three instruments have been launched into orbit with the aim of producing global maps of sea surface salinity and soil moisture using the 1400-1427 MHz band: SMOS, Aquarius and SMAP. Although this frequency band is allocated to passive measurements only, RFI (Radio-Frequency Interference) is present in the data of all three missions. On a global scale, the three sensors have observed approximately the same distribution of RFI. Japan is an important exception that has implications for the design of RFI detection algorithms. RFI in Japan is caused by a large number of emitters belonging to the same system (TV receivers) and for this reason some traditional RFI detection strategies detect little to no RFI over Japan. The study of this case has led to an improvement of the approach to detect RFI in Aquarius data.

Aquarius↗

NASA NTRS2021

Lila: Optimal Dispatching in Probabilistic Temporal Networks using Monte Carlo Tree Search

Executing a Probabilistic Simple Temporal Network (PSTN) amounts at scheduling, i.e. \textit{dispatch}, a set of events under time uncertainty. This constitutes a NP-hard online optimization problem. The right execution time must be dynamically assigned to each event of the PSTN such that the temporal constraints are met, whereas activity durations are progressively observed as the execution unfolds. We propose a dispatching algorithm based on Monte Carlo Tree Search, called Lila, with the following characteristics: (i) it is an anytime algorithm, both offline and online, proven asymptotically optimal; (ii) it returns the current probability of success, either before or at any moment during operations; (iii) it handles any possible continuous or discrete, even non-parametric, probability distributions, as well as inter-dependencies between random variables, exogenous and endogenous uncertainty; and (iv) can be easily extended to handle probabilistic external events, PSTNs with resources, PSTNs with cutoff times and precondition chains, etc. Lila is universal in the sense that it can handle any dispatching protocol, simply by specifying it to the algorithm. It has the unlimited flexibility offered by the simulation paradigm, whilst it asymptotically converges to optimal decisions and/or robustness approximations.

Chien, Steve A.↗

DOE OSTI2021

Computing partition functions in the one-clean-qubit model

We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive-semidefinite Hamiltonians, our method has an expected running-time that is almost linear in [M/( ε rel Z )] 2 , where M is the dimension of the quantum system, Z is the partition function, and ε rel is the relative precision. It is based on approximations of the exponential operator as linear combinations of certain operators related to block-encoding of Hamiltonians or Hamiltonian evolutions. The trace of each operator is estimated using a standard algorithm in the one-clean-qubit model. For large values of Z , our method may run faster than exact classical methods, whose complexities are polynomial in M . We also prove that a version of the partition function estimation problem within additive error is complete for the so-called DQC1 complexity class, suggesting that our method provides a superpolynomial speedup for certain parameter values. Overall, to attain a desired relative precision, we develop a classical procedure based on a sequence of approximations within predetermined additive errors that may be of independent interest.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2007

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

Scattered data interpolation is a problem of interest in numerous areas such as electronic imaging, smooth surface modeling, and computational geometry. Our motivation arises from applications in geology and mining, which often involve large scattered data sets and a demand for high accuracy. The method of choice is ordinary kriging. This is because it is a best unbiased estimator. Unfortunately, this interpolant is computationally very expensive to compute exactly. For n scattered data points, computing the value of a single interpolant involves solving a dense linear system of size roughly n x n. This is infeasible for large n. In practice, kriging is solved approximately by local approaches that are based on considering only a relatively small'number of points that lie close to the query point. There are many problems with this local approach, however. The first is that determining the proper neighborhood size is tricky, and is usually solved by ad hoc methods such as selecting a fixed number of nearest neighbors or all the points lying within a fixed radius. Such fixed neighborhood sizes may not work well for all query points, depending on local density of the point distribution. Local methods also suffer from the problem that the resulting interpolant is not continuous. Meyer showed that while kriging produces smooth continues surfaces, it has zero order continuity along its borders. Thus, at interface boundaries where the neighborhood changes, the interpolant behaves discontinuously. Therefore, it is important to consider and solve the global system for each interpolant. However, solving such large dense systems for each query point is impractical. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. The problems arise from the fact that the covariance functions that are used in kriging have global support. Our implementations combine, utilize, and enhance a number of different approaches that have been introduced in literature for solving large linear systems for interpolation of scattered data points. For very large systems, exact methods such as Gaussian elimination are impractical since they require 0(n(exp 3)) time and 0(n(exp 2)) storage. As Billings et al. suggested, we use an iterative approach. In particular, we use the SYMMLQ method, for solving the large but sparse ordinary kriging systems that result from tapering. The main technical issue that need to be overcome in our algorithmic solution is that the points' covariance matrix for kriging should be symmetric positive definite. The goal of tapering is to obtain a sparse approximate representation of the covariance matrix while maintaining its positive definiteness. Furrer et al. used tapering to obtain a sparse linear system of the form Ax = b, where A is the tapered symmetric positive definite covariance matrix. Thus, Cholesky factorization could be used to solve their linear systems. They implemented an efficient sparse Cholesky decomposition method. They also showed if these tapers are used for a limited class of covariance models, the solution of the system converges to the solution of the original system. Matrix A in the ordinary kriging system, while symmetric, is not positive definite. Thus, their approach is not applicable to the ordinary kriging system. Therefore, we use tapering only to obtain a sparse linear system. Then, we use SYMMLQ to solve the ordinary kriging system. We show that solving large kriging systems becomes practical via tapering and iterative methods, and results in lower estimation errors compared to traditional local approaches, and significant memory savings compared to the original global system. We also developed a more efficient variant of the sparse SYMMLQ method for large ordinary kriging systems. This approach adaptively finds the correct local neighborhood for each query point in the interpolation process.

Memarsadeghi, Nargess↗

DOE OSTI2020

Low synchronization Gram–Schmidt and generalized minimal residual algorithms

The Gram–Schmidt process uses orthogonal projection to construct the A = QR factorization of a matrix. When Q has linearly independent columns, the operator P = I - Q(QTQ)-1QT defines an orthogonal projection onto Q⊥. In finite precision, Q loses orthogonality as the factorization progresses. A family of approximate projections is derived with the form P = I - QTQT, with correction matrix T. When T = (QTQ)-1, and T is triangular, it is postulated that the best achievable orthogonality is $\mathcal{O}(ε)\mathcal{K}(A)$. We present new variants of modified (MGS) and classical Gram–Schmidt algorithms that require one global reduction step. An interesting form of the projector leads to a compact WY representation for MGS. In particular, the inverse compact WY MGS algorithm is equivalent to a lower triangular solve. Our main contribution is to introduce a backward normalization lag into the compact WY representation, resulting in a $\mathcal{O}(ε)\mathcal{K}[r_0, AV_m])$ stable Generalized Minimal Residual Method (GMRES) algorithm that requires only one global reduce per iteration. Finally, further improvements in performance are achieved by accelerating GMRES on GPUs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Performance evaluations of signed and unsigned noisy approximate quantum Fourier arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route toward a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted-sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting-qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges—relevant to signed, unsigned, modular and non-modular versions—that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze the performance trends in our results and speculate on possible future developments within this computational paradigm.

Computational models↗

NASA NTRS2024

Automatic Detection and Classification of Aurora in THEMIS All‐Sky Images

We report a novel machine-learning algorithm for automatically detecting and classifying aurora in all–sky images (ASI) that is largely trained without requiring ground–truth labels. By including a small number of labeled images, we are able to automatically label all of the approximately 700 million images in the Time History of Events and Macroscale Interactions during Substorms (THEMIS) ASI data set from 2008 to 2022. We use a two–stage approach. In the first stage, we adapt the Simple framework for Contrastive Learning of Representations (SimCLR) algorithm to learn latent representations of THEMIS all–sky images. We then finetune a classifier network on the latent representations our model learns of the manually labeled Oslo aurora THEMIS (OATH) data set. We demonstrate that this two–stage approach achieves excellent classification results on data for which there is no current ML classification benchmark. The outcome of this work will facilitate efficient information retrieval for researchers interested in specific categories of aurora and will enable large scale statistical studies and machine learning analyses of THEMIS all–sky images that have not previously been possible. To demonstrate possible ways to utilize this database, we performed a statistical analysis of the occurrence rates of auroral labels with respect to solar wind parameters, interplanetary magnetic field vector, and geomagnetic indices. We further investigate the occurrence rates of auroral phenomena in the annotated data set and their geoeffectiveness by utilizing the co–located THEMIS ground magnetometer data set.

Jeremiah W Johnson↗

NASA NTRS1989

Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations

The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.

Hafez, Mohammed↗

NASA NTRS1976

An algorithm for selecting a radiation transport subgrid for ablation and radiation coupled hypersonic viscous shock-layer problems

An algorithm is described for selecting a grid subset for calculating radiative transport. The subset spacing is determined by using the variation in aerothermal properties across the full grid of the shock layer. Results show that a radiation grid subset of 15 to 20 points can be used for viscous-shock layer calculations where approximately 50 grid points are required to define the aerothermal profiles. Results are presented for various planetary entry conditions with and without mass injection to demonstrate both the validity and utility of the algorithm.

Bolz, C. W., Jr.↗

NASA NTRS1980

Pareto-optimal multi-objective design of airplane control systems

A constrained minimization algorithm for the computer aided design of airplane control systems to meet many requirements over a set of flight conditions is generalized using the concept of Pareto-optimization. The new algorithm yields solutions on the boundary of the achievable domain in objective space in a single run, whereas the older method required a sequence of runs to approximate such a limiting solution. However, Pareto-optimality does not guarantee a satisfactory design, since such solutions may emphasize some objectives at the expense of others. The designer must still interact with the program to obtain a well-balanced set of objectives. Using the example of a fighter lateral stability augmentation system (SAS) design over five flight conditions, several effective techniques are developed for obtaining well-balanced Pareto-optimal solutions. For comparison, one of these techniques is also used in a recently developed algorithm of Kreisselmeier and Steinhauser, which replaces the hard constraints with soft constraints, using a special penalty function. It is shown that comparable results can be obtained.

Schy, A. A.↗