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NASA NTRS2001

The Computational Complexity, Parallel Scalability, and Performance of Atmospheric Data Assimilation Algorithms

The computational complexity of algorithms for Four Dimensional Data Assimilation (4DDA) at NASA's Data Assimilation Office (DAO) is discussed. In 4DDA, observations are assimilated with the output of a dynamical model to generate best-estimates of the states of the system. It is thus a mapping problem, whereby scattered observations are converted into regular accurate maps of wind, temperature, moisture and other variables. The DAO is developing and using 4DDA algorithms that provide these datasets, or analyses, in support of Earth System Science research. Two large-scale algorithms are discussed. The first approach, the Goddard Earth Observing System Data Assimilation System (GEOS DAS), uses an atmospheric general circulation model (GCM) and an observation-space based analysis system, the Physical-space Statistical Analysis System (PSAS). GEOS DAS is very similar to global meteorological weather forecasting data assimilation systems, but is used at NASA for climate research. Systems of this size typically run at between 1 and 20 gigaflop/s. The second approach, the Kalman filter, uses a more consistent algorithm to determine the forecast error covariance matrix than does GEOS DAS. For atmospheric assimilation, the gridded dynamical fields typically have More than 10(exp 6) variables, therefore the full error covariance matrix may be in excess of a teraword. For the Kalman filter this problem can easily scale to petaflop/s proportions. We discuss the computational complexity of GEOS DAS and our implementation of the Kalman filter. We also discuss and quantify some of the technical issues and limitations in developing efficient, in terms of wall clock time, and scalable parallel implementations of the algorithms.

Lyster, Peter M.↗

NASA NTRS2013

The Role of Model and Initial Condition Error in Numerical Weather Forecasting Investigated with an Observing System Simulation Experiment

A series of experiments that explore the roles of model and initial condition error in numerical weather prediction are performed using an observing system simulation experiment (OSSE) framework developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office (NASA/GMAO). The use of an OSSE allows the analysis and forecast errors to be explicitly calculated, and different hypothetical observing networks can be tested with ease. In these experiments, both a full global OSSE framework and an 'identical twin' OSSE setup are utilized to compare the behavior of the data assimilation system and evolution of forecast skill with and without model error. The initial condition error is manipulated by varying the distribution and quality of the observing network and the magnitude of observation errors. The results show that model error has a strong impact on both the quality of the analysis field and the evolution of forecast skill, including both systematic and unsystematic model error components. With a realistic observing network, the analysis state retains a significant quantity of error due to systematic model error. If errors of the analysis state are minimized, model error acts to rapidly degrade forecast skill during the first 24-48 hours of forward integration. In the presence of model error, the impact of observation errors on forecast skill is small, but in the absence of model error, observation errors cause a substantial degradation of the skill of medium range forecasts.

Model Error↗

NASA NTRS2020

ANC of Radiated Sound from a Small UAS Rotor using Virtual Error Sensors

Small unmanned aerial systems (UAS) are becoming increasingly common for private, military, and commercial use, increasing community noise exposure. Reducing the noise produced by UAS could help improve community acceptance. Active noise control (ANC) might be used to attenuate noise produced by UAS, however, traditional ANC systems require a physical sensor in the far-field, which is not feasible. This paper assesses a virtual error sensing (VES) method that eliminates the need for a far-field sensor. This paper describes the proposed VES strategy, and presents numerical simulations and experimental results that highlight the benefits and limitations of the approach. Results for the VES system alone and with an ANC approach are presented and discussed. Experimental testing focused on attenuating the tonal noise produced by one 2-bladed rotor with a tip radius of 11.9 cm. Pressure variations caused by blade rotation were measured in the near and far-field using electret microphones and externally polarized condenser microphones, respectively. The filtered-x least mean squares algorithm was used in conjunction with the VES system to attenuate the far-field response. Experimental results show reductions between 6-13 dB at varying far-field locations and rotation rates.

virtual error sensor↗

DOE OSTI2017

Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields

In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic (B field) confinement. However, the best available a priori procedure for composing highly accurate AGTO sets for atoms in a strong B field [W. Zhu et al., Phys. Rev. A 90, 022504 (2014)] yields very large basis sets. Their size is problematical for use in any calculation with unfavorable computational cost scaling. Here we provide an alternative constructive procedure. It is based upon analysis of the underlying physics of atoms in B fields that allow identification of several principles for the construction of AGTO basis sets. Aided by numerical optimization and parameter fitting, followed by fine tuning of fitting parameters, we devise formulae for generating accurate AGTO basis sets in an arbitrary B field. For the hydrogen iso-electronic sequence, a set depends on B field strength, nuclear charge, and orbital quantum numbers. For multi-electron systems, the basis set formulae also include adjustment to account for orbital occupations. Tests of the new basis sets for atoms H through C (1 ≤ Z ≤ 6) and ions Li+, Be+, and B+, in a wide B field range (0 ≤ B ≤ 2000 a.u.), show an accuracy better than a few μhartree for single-electron systems and a few hundredths to a few mHs for multi-electron atoms. The relative errors are similar for different atoms and ions in a large B field range, from a few to a couple of tens of millionths, thereby confirming rather uniform accuracy across the nuclear charge Z and B field strength values. Residual basis set errors are two to three orders of magnitude smaller than the electronic correlation energies in multi-electron atoms, a signal of the usefulness of the new AGTO basis sets in correlated wavefunction or density functional calculations for atomic and molecular systems in an external strong B field

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1990

Orbit determination and gravitational field accuracy for a Mercury transponder satellite

Covariance studies were performed to investigate the orbit determination problem for a small transponder satellite in a nearly circular polar orbit with 4-hour period around Mercury. With X band and Ka band Doppler and range measurements, the analysis indicates that the gravitational field through degree and order 10 can be solved for from as few as 40 separate 8-hour arcs of tracking data. In addition, the earth-Mercury distance can be determined during each ranging period with about 6-cm accuracy. The expected geoid accuracy is 10 cm up through degree 5, and 1 m through degree 8. The main error sources were the geocentric range measurement error, the uncertainties in higher degree gravity field terms, which were not solved for, and the solar radiation pressure uncertainty.

Vincent, Mark A.↗

NASA NTRS1981

Influence of gravity field uncertainties on the results from POGO and Magsat geomagnetic surveys

Errors in the gravity models used in satellite position calculations are examined as a possible source of the 0 to 100% variance found between POGO and Magsat magnetic data and the extrapolations of aerial magnetic survey data to satellite heights. For POGO data obtained over the New York Bight region using a relatively poor gravity field (a hybrid spherical harmonic model of degree 7 and order 6 with three higher order resonance terms), the magnitude of the error in the satellite height component is found to be sufficient to account for the amplitude of the discrepancy, however the frequency of the quasi-periodic orbital error is too large to explain the localized nature of the differences. For the case of the Magsat satellite, in which a more accurate gravity model was used, it is found that a 30 mgal gravitational anomaly distributed over a 5 x 5 deg area will produce insufficiently large position errors to account for the variations. The agreement between the two sets of satellite data in the New York Bight region suggests either a consistent error in satellite measurements, or problems with the reduction and processing of the aeromagnetic data.

Taylor, P. T.↗

NASA NTRS2011

Modeling the Height of Young Forests Regenerating from Recent Disturbances in Mississippi using Landsat and ICESat data

Many forestry and earth science applications require spatially detailed forest height data sets. Among the various remote sensing technologies, lidar offers the most potential for obtaining reliable height measurement. However, existing and planned spaceborne lidar systems do not have the capability to produce spatially contiguous, fine resolution forest height maps over large areas. This paper describes a Landsat-lidar fusion approach for modeling the height of young forests by integrating historical Landsat observations with lidar data acquired by the Geoscience Laser Altimeter System (GLAS) instrument onboard the Ice, Cloud, and land Elevation (ICESat) satellite. In this approach, "young" forests refer to forests reestablished following recent disturbances mapped using Landsat time-series stacks (LTSS) and a vegetation change tracker (VCT) algorithm. The GLAS lidar data is used to retrieve forest height at sample locations represented by the footprints of the lidar data. These samples are used to establish relationships between lidar-based forest height measurements and LTSS-VCT disturbance products. The height of "young" forest is then mapped based on the derived relationships and the LTSS-VCT disturbance products. This approach was developed and tested over the state of Mississippi. Of the various models evaluated, a regression tree model predicting forest height from age since disturbance and three cumulative indices produced by the LTSS-VCT method yielded the lowest cross validation error. The R(exp 2) and root mean square difference (RMSD) between predicted and GLAS-based height measurements were 0.91 and 1.97 m, respectively. Predictions of this model had much higher errors than indicated by cross validation analysis when evaluated using field plot data collected through the Forest Inventory and Analysis Program of USDA Forest Service. Much of these errors were due to a lack of separation between stand clearing and non-stand clearing disturbances in current LTSS-VCT products and difficulty in deriving reliable forest height measurements using GLAS samples when terrain relief was present within their footprints. In addition, a systematic underestimation of about 5 m by the developed model was also observed, half of which could be explained by forest growth that occurred between field measurement year and model target year. The remaining difference suggests that tree height measurements derived using waveform lidar data could be significantly underestimated, especially for young pine forests. Options for improving the height modeling approach developed in this study were discussed.

Li, Ainong↗

NASA NTRS1995

Error in predicting hydrosol backscattering from remotely sensed reflectance

Monte Carlo simulations are carried out to determine the error in the inversion of backscattering from remotely sensed reflectance when geometrical shape factors of the light field are assumed to be unity. The results show that error in backscattering inversion can vary from a 40% overestimation to a 20% underestimation and is dependent on the solar angle and the hydrosol consituents contributing to backscattering. The simulations also demostrate that for chlorophyll concentrations ranging from 0.05 to 20 mg/cu m the most dramatic change in the geometrical shape factors occurs near 1.0 to 1.5 mg/cu m chlorophyll. The potential importance of bacteria in influencing the shape factor and the subsequent effect of bacteria on the retrieval of the backscattering from remote sensing reflectance are shown. Quartzlike material's strong impact on geometrical shape factors and errors of retrieval of backscattering at low chlorophyll concentrations are also demonstrated. Remote sensing reflectance inversion schemes must include information about the backscattering function to be successful.

Weidemann, A. D.↗

DOE OSTI2013

Precise measurement of the transverse piezoelectric coefficient for thin films on anisotropic substrate

In this study, we propose a reliable measurement method for the effective transverse piezoelectric coefficient for thin films especially on anisotropic substrate. This coefficient for piezoelectric Pb(Zr, Ti)O{sub 3} (PZT) thin films was calculated by measuring the electric field-induced tip displacement of unimorph cantilevers composed of PZT thin films and Si substrates. We evaluated the reliability of the proposed measurement method by comparing it with numerical analysis and confirmed that the relative error of the piezoelectric coefficient (e{sub 31,f}) was less than 1%. We prepared 16 different unimorph cantilevers composed of identical PZT films on different Si beam geometries that had various substrate thicknesses and cantilever widths. Although the effective transverse piezoelectric coefficient e{sub 31,f} of PZT thin films ranged from -6.5 to -14 C/m{sup 2} as a function of the applied voltage, the difference among the 16 samples with an applied voltage of 25 V was within 10%. These results demonstrate that the proposed measurement method has sufficient reliability and can be used to evaluate the effective transverse piezoelectric coefficient e{sub 31,f} of thin films.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2008

Coaxial Electric Heaters

Coaxial electric heaters have been conceived for use in highly sensitive instruments in which there are requirements for compact heaters but stray magnetic fields associated with heater electric currents would adversely affect operation. Such instruments include atomic clocks and magnetometers that utilize heated atomic-sample cells, wherein stray magnetic fields at picotesla levels could introduce systematic errors into instrument readings. A coaxial electric heater is essentially an axisymmetric coaxial cable, the outer conductor of which is deliberately made highly electrically resistive so that it can serve as a heating element. As in the cases of other axisymmetric coaxial cables, the equal magnitude electric currents flowing in opposite directions along the inner and outer conductors give rise to zero net magnetic field outside the outer conductor. Hence, a coaxial electric heater can be placed near an atomic-sample cell or other sensitive device. A coaxial electric heater can be fabricated from an insulated copper wire, the copper core of which serves as the inner conductor. For example, in one approach, the insulated wire is dipped in a colloidal graphite emulsion, then the emulsion-coated wire is dried to form a thin, uniform, highly electrically resistive film that serves as the outer conductor. Then the film is coated with a protective layer of high-temperature epoxy except at the end to be electrically connected to the power supply. Next, the insulation is stripped from the wire at that end. Finally, electrical leads from the heater power supply are attached to the exposed portions of the wire and the resistive film. The resistance of the graphite film can be tailored via its thickness. Alternatively, the film can be made from an electrically conductive paint, other than a colloidal graphite emulsion, chosen to impart the desired resistance. Yet another alternative is to tailor the resistance of a graphite film by exploiting the fact that its resistance can be changed permanently within about 10 percent by heating it to a temperature above 300 C. A coaxial heater, with electrical leads attached, that has been bent into an almost full circle for edge heating of a circular window is shown. (In the specific application, there is a requirement for a heated cell window, through which an optical beam enters the cell.)

Strekalov, Dmitry↗

DOE OSTI2021

Functional Principal Component Analysis of Radio–Optical Reference Frame Tie

The Gaia optical reference frame is intrinsically undefined with respect to global orientation and spin, so it needs to be anchored in the radio-based International Celestial Reference Frame (ICRF) to provide a referenced and quasi-inertial celestial coordinate system. The link between the two fundamental frames is realized through two samples of distant extragalactic sources, mostly active galactic nuclei and quasars, but only the smaller sample of radio-loud ICRF sources with optical counterparts is available to determine the mutual orientation. The robustness of this link can be mathematically formulated in the framework of functional principal component analysis using a set of vector spherical harmonics to represent the differences in celestial positions of the common objects. The weakest eigenvectors are computed, which describe the greatest deficiency of the link. The deficient or poorly determined terms are specific vector fields on the sphere that carry the largest errors of absolute astrometry using Gaia in reference to the ICRF. This analysis provides guidelines for the future development of the ICRF maximizing the accuracy of the link over the entire celestial sphere. A measure of the robustness of a least-squares solution, which can be applied to any linear model fitting problem, is introduced to help discriminate between reference frame tie models of different degrees.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1995

Clouds and the Earth's Radiant Energy System (CERES) algorithm theoretical basis document: Overviews (subsystem 0) - Volume 1

The theoretical bases for the Release 1 algorithms that will be used to process satellite data for investigation of the Clouds and the Earth's Radiant Energy System (CERES) are described. The architecture for software implementation of the methodologies is outlined. Volume 1 provides both summarized and detailed overviews of the CERES Release 1 data analysis system. CERES will produce global top-of-the-atmosphere shortwave and longwave radiative fluxes at the top of the atmosphere, at the surface, and within the atmosphere by using the combination of a large variety of measurements and models. The CERES processing system includes radiance observations from CERES scanning radiometers, cloud properties derived from coincident satellite imaging radiometers, temperature and humidity fields from meteorological analysis models, and high-temporal-resolution geostationary satellite radiances to account for unobserved times. CERES will provide a continuation of the ERBE record and the lowest error climatology of consistent cloud properties and radiation fields. CERES will also substantially improve our knowledge of the Earth's surface radiation budget.

Wielicki, Bruce A.↗

DOE OSTI2016

Quantitative measurement for the microstructural parameters of nano-precipitates in Al-Mg-Si-Cu alloys

Size, number density and volume fraction of nano-precipitates are important microstructural parameters controlling the strengthening of materials. In this work a widely accessible, convenient, moderately time efficient method with acceptable accuracy and precision has been provided for measurement of volume fraction of nano-precipitates in crystalline materials. The method is based on the traditional but highly accurate technique of measuring foil thickness via convergent beam electron diffraction. A new equation is proposed and verified with the aid of 3-dimensional atom probe (3DAP) analysis, to compensate for the additional error resulted from the hardly distinguishable contrast of too short incomplete precipitates cut by the foil surface. The method can be performed on a regular foil specimen with a modern LaB{sub 6} or field-emission-gun transmission electron microscope. Precisions around ± 16% have been obtained for precipitate volume fractions of needle-like β″/C and Q precipitates in an aged Al-Mg-Si-Cu alloy. The measured number density is close to that directly obtained using 3DAP analysis by a misfit of 4.5%, and the estimated precision for number density measurement is about ± 11%. The limitations of the method are also discussed. - Highlights: •A facile method for measuring volume fraction of nano-precipitates based on CBED •An equation to compensate for small invisible precipitates, with 3DAP verification •Precisions around ± 16% for volume fraction and ± 11% for number density.

36 MATERIALS SCIENCE↗

NASA NTRS1997

Distortion Representation of Forecast Errors for Model Skill Assessment and Objective Analysis

We proposed a novel characterization of errors for numerical weather predictions. In its simplest form we decompose the error into a part attributable to phase errors and a remainder. The phase error is represented in the same fashion as a velocity field and is required to vary slowly and smoothly with position. A general distortion representation allows for the displacement and amplification or bias correction of forecast anomalies. Characterizing and decomposing forecast error in this way has two important applications, which we term the assessment application and the objective analysis application. For the assessment application, our approach results in new objective measures of forecast skill which are more in line with subjective measures of forecast skill and which are useful in validating models and diagnosing their shortcomings. With regard to the objective analysis application, meteorological analysis schemes balance forecast error and observational error to obtain an optimal analysis. Presently, representations of the error covariance matrix used to measure the forecast error are severely limited. For the objective analysis application our approach will improve analyses by providing a more realistic measure of the forecast error. We expect, a priori, that our approach should greatly improve the utility of remotely sensed data which have relatively high horizontal resolution, but which are indirectly related to the conventional atmospheric variables. In this project, we are initially focusing on the assessment application, restricted to a realistic but univariate 2-dimensional situation. Specifically, we study the forecast errors of the sea level pressure (SLP) and 500 hPa geopotential height fields for forecasts of the short and medium range. Since the forecasts are generated by the GEOS (Goddard Earth Observing System) data assimilation system with and without ERS 1 scatterometer data, these preliminary studies serve several purposes. They (1) provide a testbed for the use of the distortion representation of forecast errors, (2) act as one means of validating the GEOS data assimilation system and (3) help to describe the impact of the ERS 1 scatterometer data.

Hoffman, Ross N.↗

DOE OSTI2015

Optimization of an on-board imaging system for extremely rapid radiation therapy

Purpose: Next-generation extremely rapid radiation therapy systems could mitigate the need for motion management, improve patient comfort during the treatment, and increase patient throughput for cost effectiveness. Such systems require an on-board imaging system that is competitively priced, fast, and of sufficiently high quality to allow good registration between the image taken on the day of treatment and the image taken the day of treatment planning. In this study, three different detectors for a custom on-board CT system were investigated to select the best design for integration with an extremely rapid radiation therapy system. Methods: Three different CT detectors are proposed: low-resolution (all 4 × 4 mm pixels), medium-resolution (a combination of 4 × 4 mm pixels and 2 × 2 mm pixels), and high-resolution (all 1 × 1 mm pixels). An in-house program was used to generate projection images of a numerical anthropomorphic phantom and to reconstruct the projections into CT datasets, henceforth called “realistic” images. Scatter was calculated using a separate Monte Carlo simulation, and the model included an antiscatter grid and bowtie filter. Diagnostic-quality images of the phantom were generated to represent the patient scan at the time of treatment planning. Commercial deformable registration software was used to register the diagnostic-quality scan to images produced by the various on-board detector configurations. The deformation fields were compared against a “gold standard” deformation field generated by registering initial and deformed images of the numerical phantoms that were used to make the diagnostic and treatment-day images. Registrations of on-board imaging system data were judged by the amount their deformation fields differed from the corresponding gold standard deformation fields—the smaller the difference, the better the system. To evaluate the registrations, the pointwise distance between gold standard and realistic registration deformation fields was computed. Results: By most global metrics (e.g., mean, median, and maximum pointwise distance), the high-resolution detector had the best performance but the medium-resolution detector was comparable. For all medium- and high-resolution detector registrations, mean error between the realistic and gold standard deformation fields was less than 4 mm. By pointwise metrics (e.g., tracking a small lesion), the high- and medium-resolution detectors performed similarly. For these detectors, the smallest error between the realistic and gold standard registrations was 0.6 mm and the largest error was 3.6 mm. Conclusions: The medium-resolution CT detector was selected as the best for an extremely rapid radiation therapy system. In essentially all test cases, data from this detector produced a significantly better registration than data from the low-resolution detector and a comparable registration to data from the high-resolution detector. The medium-resolution detector provides an appropriate compromise between registration accuracy and system cost.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1988

Propagation of quasiplane waves along an impedance boundary

The parabolic approximation for the acoustic equations of motion is applied to the study of the sound field generated by a time harmonic plane wave at grazing incidence to a finite impedance boundary. The resulting equations possess a solution which may be expressed in terms of the complementary error function. Asymptotic expansion of this solution for field points near the boundary provides results compatible with those for a point source on the boundary for both the soft boundary (finite impedance) and hard boundary (the limit in which the impedance becomes infinite) cases. The presence of a surface wave in the solution is also established.

Mcaninch, G. L.↗

NASA NTRS2002

On the Choice of Variable for Atmospheric Moisture Analysis

The implications of using different control variables for the analysis of moisture observations in a global atmospheric data assimilation system are investigated. A moisture analysis based on either mixing ratio or specific humidity is prone to large extrapolation errors, due to the high variability in space and time of these parameters and to the difficulties in modeling their error covariances. Using the logarithm of specific humidity does not alleviate these problems, and has the further disadvantage that very dry background estimates cannot be effectively corrected by observations. Relative humidity is a better choice from a statistical point of view, because this field is spatially and temporally more coherent and error statistics are therefore easier to obtain. If, however, the analysis is designed to preserve relative humidity in the absence of moisture observations, then the analyzed specific humidity field depends entirely on analyzed temperature changes. If the model has a cool bias in the stratosphere this will lead to an unstable accumulation of excess moisture there. A pseudo-relative humidity can be defined by scaling the mixing ratio by the background saturation mixing ratio. A univariate pseudo-relative humidity analysis will preserve the specific humidity field in the absence of moisture observations. A pseudorelative humidity analysis is shown to be equivalent to a mixing ratio analysis with flow-dependent covariances. In the presence of multivariate (temperature-moisture) observations it produces analyzed relative humidity values that are nearly identical to those produced by a relative humidity analysis. Based on a time series analysis of radiosonde observed-minus-background differences it appears to be more justifiable to neglect specific humidity-temperature correlations (in a univariate pseudo-relative humidity analysis) than to neglect relative humidity-temperature correlations (in a univariate relative humidity analysis). A pseudo-relative humidity analysis is easily implemented in an existing moisture analysis system, by simply scaling observed-minus background moisture residuals prior to solving the analysis equation, and rescaling the analyzed increments afterward.

Dee, Dick P.↗

NASA NTRS2015

New Developments in FPGA: SEUs and Fail-Safe Strategies from the NASA Goddard Perspective

It has been shown that, when exposed to radiation environments, each Field Programmable Gate Array (FPGA) device has unique error signatures. Subsequently, fail-safe and mitigation strategies will differ per FPGA type. In this session several design approaches for safe systems will be presented. It will also explore the benefits and limitations of several mitigation techniques. The intention of the presentation is to provide information regarding FPGA types, their susceptibilities, and proven fail-safe strategies; so that users can select appropriate mitigation and perform the required trade for system insertion. The presentation will describe three types of FPGA devices and their susceptibilities in radiation environments.

hardware description language (HDL)↗