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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Sparsely Sampled Phase-Insensitive Ultrasonic Transducer Arrays

Three methods of interpretation of outputs from sparsely sampled two-dimensional array of receiving ultrasonic transducers used in transmission experiments investigated. Methods are: description of sampled beam in terms of first few spatial moments of sampled distribution of energy; use of signal-dependent cutoff to limit extent of effective receiver aperture; and use of spatial interpolation to increase apparent density of sampling during computation. Methods reduce errors in computations of shapes of ultrasonic beams.

Patrick H. Johnston↗
NASA NTRS2011

Efficient Kriging Algorithms

More efficient versions of an interpolation method, called kriging, have been introduced in order to reduce its traditionally high computational cost. Written in C++, these approaches were tested on both synthetic and real data. Kriging is a best unbiased linear estimator and suitable for interpolation of scattered data points. Kriging has long been used in the geostatistic and mining communities, but is now being researched for use in the image fusion of remotely sensed data. This allows a combination of data from various locations to be used to fill in any missing data from any single location. To arrive at the faster algorithms, sparse SYMMLQ iterative solver, covariance tapering, Fast Multipole Methods (FMM), and nearest neighbor searching techniques were used. These implementations were used when the coefficient matrix in the linear system is symmetric, but not necessarily positive-definite.

Memarsadeghi, Nargess↗
NASA NTRS2006

Temperature-dependent Absolute Refractive Index Measurements of Synthetic Fused Silica

Using the Cryogenic, High-Accuracy Refraction Measuring System (CHARMS) at NASA's Goddard Space Flight Center, we have measured the absolute refractive index of five specimens taken from a very large boule of Corning 7980 fused silica from temperatures ranging from 30 to 310 K at wavelengths from 0.4 to 2.6 microns with an absolute uncertainty of plus or minus 1 x 10 (exp -5). Statistical variations in derived values of the thermo-optic coefficient (dn/dT) are at the plus or minus 2 x 10 (exp -8)/K level. Graphical and tabulated data for absolute refractive index, dispersion, and thermo-optic coefficient are presented for selected wavelengths and temperatures along with estimates of uncertainty in index. Coefficients for temperature-dependent Sellmeier fits of measured refractive index are also presented to allow accurate interpolation of index to other wavelengths and temperatures. We compare our results to those from an independent investigation (which used an interferometric technique for measuring index changes as a function of temperature) whose samples were prepared from the same slugs of material from which our prisms were prepared in support of the Kepler mission. We also compare our results with sparse cryogenic index data from measurements of this material from the literature.

Leviton, Douglas B.↗
NASA NTRS1973

Determination of stratospheric temperature and height gradients from Nimbus 3 radiation data

To improve the specification of stratospheric, horizontal, temperature and geopotential height fields needed for high-flying aircraft, we derived a technique to estimate data between satellite tracks using interpolated infrared interferometer spectrometer 15-micron radiation data from Nimbus 3. The interpolation is based on the observed gradients of the medium resolution infrared 15-micron radiances between subsatellite tracks. The technique was verified with radiosonde data taken within 6 hr of the satellite data. Comparison indicates that the technique developed here produces analyses that are in general agreement with those from radiosonde data. In addition, this technique provides details over areas of sparse data not shown by conventional techniques.

Nicholas, G. W.↗
NASA NTRS1990

Motion detection in astronomical and ice floe images

Two approaches are presented for establishing correspondence between small areas in pairs of successive images for motion detection. The first one, based on local correlation, is used on a pair of successive Voyager images of the Jupiter which differ mainly in locally variable translations. This algorithm is implemented on a sequential machine (VAX 780) as well as the Massively Parallel Processor (MPP). In the case of the sequential algorithm, the pixel correspondence or match is computed on a sparse grid of points using nonoverlapping windows (typically 11 x 11) by local correlations over a predetermined search area. The displacement of the corresponding pixels in the two images is called the disparities to cubic surfaces. The disparities at points where the error between the computed values and the surface values exceeds a particular threshold are replaced by the surface values. A bilinear interpolation is then used to estimate disparities at all other pixels between the grid points. When this algorithm was applied at the red spot in the Jupiter image, the rotating velocity field of the storm was determined. The second method of motion detection is applicable to pairs of images in which corresponding areas can experience considerable translation as well as rotation.

Manohar, M.↗
NASA NTRS1990

Distributed memory approaches for robotic neural controllers

The suitability is explored of two varieties of distributed memory neutral networks as trainable controllers for a simulated robotics task. The task requires that two cameras observe an arbitrary target point in space. Coordinates of the target on the camera image planes are passed to a neural controller which must learn to solve the inverse kinematics of a manipulator with one revolute and two prismatic joints. Two new network designs are evaluated. The first, radial basis sparse distributed memory (RBSDM), approximates functional mappings as sums of multivariate gaussians centered around previously learned patterns. The second network types involved variations of Adaptive Vector Quantizers or Self Organizing Maps. In these networks, random N dimensional points are given local connectivities. They are then exposed to training patterns and readjust their locations based on a nearest neighbor rule. Both approaches are tested based on their ability to interpolate manipulator joint coordinates for simulated arm movement while simultaneously performing stereo fusion of the camera data. Comparisons are made with classical k-nearest neighbor pattern recognition techniques.

Jorgensen, Charles C.↗
NASA NTRS2010

Transfer of Satellite Rainfall Uncertainty from Gauged to Ungauged Regions at Regional and Seasonal Timescales

Hydrologists and other users need to know the uncertainty of the satellite rainfall data sets across the range of time/space scales over the whole domain of the data set. Here, uncertainty' refers to the general concept of the deviation' of an estimate from the reference (or ground truth) where the deviation may be defined in multiple ways. This uncertainty information can provide insight to the user on the realistic limits of utility, such as hydrologic predictability, that can be achieved with these satellite rainfall data sets. However, satellite rainfall uncertainty estimation requires ground validation (GV) precipitation data. On the other hand, satellite data will be most useful over regions that lack GV data, for example developing countries. This paper addresses the open issues for developing an appropriate uncertainty transfer scheme that can routinely estimate various uncertainty metrics across the globe by leveraging a combination of spatially-dense GV data and temporally sparse surrogate (or proxy) GV data, such as the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar and the Global Precipitation Measurement (GPM) mission Dual-Frequency Precipitation Radar. The TRMM Multi-satellite Precipitation Analysis (TMPA) products over the US spanning a record of 6 years are used as a representative example of satellite rainfall. It is shown that there exists a quantifiable spatial structure in the uncertainty of satellite data for spatial interpolation. Probabilistic analysis of sampling offered by the existing constellation of passive microwave sensors indicate that transfer of uncertainty for hydrologic applications may be effective at daily time scales or higher during the GPM era. Finally, a commonly used spatial interpolation technique (kriging), that leverages the spatial correlation of estimation uncertainty, is assessed at climatologic, seasonal, monthly and weekly timescales. It is found that the effectiveness of kriging is sensitive to the type of uncertainty metric, time scale of transfer and the density of GV data within the transfer domain. Transfer accuracy is lowest at weekly timescales with the error doubling from monthly to weekly.However, at very low GV data density (<20% of the domain), the transfer accuracy is too low to show any distinction as a function of the timescale of transfer.

Tang, Ling↗
NASA NTRS2021

Probabilistic Machine Learning Estimation of Ocean Mixed Layer Depth from Dense Satellite and Sparse In-Situ Observations

The ocean mixed layer plays an important role in the coupling between the upper ocean and atmosphere across a wide range of time scales. Estimation of the variability of the ocean mixed layer is therefore important for atmosphere-ocean prediction and analysis. The increasing coverage of in situ Argo profile data allows for an increasingly accurate analysis of the mixed layer depth (MLD) variability associated with deviations from the seasonal climatology. However, sampling rates are not sufficient to fully resolve subseasonal (<90 day) MLD variability. Yet, many multivariate observations-based analyses include implicit modeled subseasonal MLD variability. One analysis method is optimal interpolation of in situ data, but the interior analysis can be improved by leveraging surface data with regression or variational approaches. Here, we demonstrate how machine learning methods and satellite sea surface temperature, salinity, and height facilitate MLD estimation in a pilot study of two regions: the mid-latitude southern Indian and the eastern equatorial Pacific Oceans. We construct multiple machine learning architectures to produce weekly 1/2° gridded MLD anomaly fields (relative to a monthly climatology) with uncertainty estimates. We test multiple traditional and probabilistic machine learning techniques to compare both accuracy and probabilistic calibration. We validate our methodology by applying it to ocean model simulations. We find that incorporating sea surface data through a machine learning model improves the performance of spatiotemporal MLD variability estimation compared to optimal interpolation of Argo observations alone. These preliminary results are a promising first step for the application of machine learning to MLD prediction.

Machine Learning↗
NASA NTRS1981

Optimal interpolation and the Kalman filter

The estimation theory of stochastic-dynamic systems is described and used in a numerical study of optimal interpolation. The general form of data assimilation methods is reviewed. The Kalman-Bucy, KB filter, and optimal interpolation (OI) filters are examined for effectiveness in performance as gain matrices using a one-dimensional form of the shallow-water equations. Control runs in the numerical analyses were performed for a ten-day forecast in concert with the OI method. The effects of optimality, initialization, and assimilation were studied. It was found that correct initialization is necessary in order to localize errors, especially near boundary points. Also, the use of small forecast error growth rates over data-sparse areas was determined to offset inaccurate modeling of correlation functions near boundaries.

Cohn, S.↗
NASA NTRS2017

Development and Assessment of the SMAP Enhanced Passive Soil Moisture Product

Launched in January 2015, the National Aeronautics and Space Administration (NASA) Soil Moisture Active Passive (SMAP) observatory was designed to provide frequent global mapping of high-resolution soil moisture and freeze-thaw state every two to three days using a radar and a radiometer operating at L-band frequencies. Despite a hardware mishap that rendered the radar inoperable shortly after launch, the radiometer continues to operate nominally, returning more than two years of science data that have helped to improve existing hydrological applications and foster new ones.Beginning in late 2016 the SMAP project launched a suite of new data products with the objective of recovering some high-resolution observation capability loss resulting from the radar malfunction. Among these new data products are the SMAP Enhanced Passive Soil Moisture Product that was released in December 2016, followed by the SMAPSentinel-1 Active-Passive Soil Moisture Product in April 2017.This article covers the development and assessment of the SMAP Level 2 Enhanced Passive Soil Moisture Product (L2_SM_P_E). The product distinguishes itself from the current SMAP Level 2 Passive Soil Moisture Product (L2_SM_P) in that the soil moisture retrieval is posted on a 9 km grid instead of a 36 km grid. This is made possible by first applying the Backus-Gilbert optimal interpolation technique to the antenna temperature (TA) data in the original SMAP Level 1B Brightness Temperature Product to take advantage of the overlapped radiometer footprints on orbit. The resulting interpolated TA data then go through various correctioncalibration procedures to become the SMAP Level 1C Enhanced Brightness Temperature Product (L1C_TB_E). The L1C_TB_E product, posted on a 9 km grid, is then used as the primary input to the current operational SMAP baseline soil moisture retrieval algorithm to produce L2_SM_P_E as the final output. Images of the new product reveal enhanced visual features that are not apparent in the standard product. Based on in situ data from core validation sites and sparse networks representing different seasons and biomes all over the world, comparisons between L2_SM_P_E and in situ data were performed for the duration of April 1, 2015 October 30, 2016. It was found that the performance of the enhanced 9 km L2_SM_P_E is equivalent to that of the standard 36 km L2_SM_P, attaining a retrieval uncertainty below 0.040 m(exp 3)/m(exp 3) unbiased root-mean-square error (ubRMSE) and a correlation coefficient above 0.800. This assessment also affirmed that the Single Channel Algorithm using the V-polarized TB channel (SCA-V) delivered the best retrieval performance among the various algorithms implemented for L2_SM_P_E, a result similar to a previous assessment for L2_SM_P.

Enhanced↗
NASA NTRS1989

Totally parallel multilevel algorithms for sparse elliptic systems

The fastest known algorithms for the solution of a large elliptic boundary value problem on a massively parallel hypercube all require O(log(n)) floating point operations and O(log(n)) distance-1 communications, if massively parallel is defined to mean a number of processors proportional to the size n of the problem. The Totally Parallel Multilevel Algorithm (TPMA) that has, as special cases, four of these fast algorithms is described. These four algorithms are Parallel Superconvergent Multigrid (PSMG), Robust Multigrid, the Fast Fourier Transformation (FFT) based Spectral Algorithm, and Parallel Cyclic Reduction. The algorithm TPMA, when described recursively, has four steps: (1) project to a collection of interlaced, coarser problems at the next lower level; (2) apply TPMA, recursively, to each of these lower level problems, solving directly at the lowest level; (3) interpolate these approximate solutions to the finer grid, and to verage them to form an approximate solution on this grid; and (4) refine this approximate solution with a defect-correction step, using a local approximate inverse. Choice of the projection operator (P), the interpolation operator (Q), and the smoother (S) determines the class of problems on which TPMA is most effective. There are special cases in which the first three steps produce an exact solution, and the smoother is not needed (e.g., constant coefficient operators).

Frederickson, Paul O.↗
NASA NTRS2019

Diurnal Cycle of IMERG V06 Precipitation

This study demonstrates the maturing ability of the half-hourly precipitation estimates from the Integrated Multi-satellitE Retrievals for GPM (IMERG) for use in global analyses of the diurnal cycle. The refined intercalibration and interpolation between the sensors in V06 leads to greater consistency in the precipitation retrievals over different hours of the day. Evaluation against ground measurements suggests a slight lag in the diurnal phase of only +0.59 h. We demonstrate the diurnal cycle over different regions around the globe, including the Maritime Continent, where accurate representation of precipitation variability in global models remains a challenge. Using examples over Singapore, Bangladesh, and Lake Victoria, we reveal the intricate interplay between diurnal and seasonal variability. This study demonstrates the unprecedented capability of IMERG in capturing the diurnal cycle of precipitation globally, potentially advancing our understanding in regions of sparse ground measurements and supporting improvements in its representation in global models.

Jackson Tan↗
NASA NTRS2003

Characterization of the Crab Pulsar's Timing Noise

We present a power spectral analysis of the Crab pulsar's timing noise, mainly using radio measurements from Jodrell Bank taken over the period 1982-1989, an interval bounded by sparse data sampling and a large glitch. The power spectral analysis is complicated by nonuniform data sampling and the presence of a steep red power spectrum that can distort power spectra measurement by causing severe power 'leakage'. We develop a simple windowing method for computing red noise power spectra of uniformly sampled data sets and test it on Monte Carlo generated sample realizations of red power-law noise. We generalize time-domain methods of generating power-law red noise with even integer spectral indices to the case of noninteger spectral indices. The Jodrell Bank pulse phase residuals are dense and smooth enough that an interpolation onto a uniform time series is possible. A windowed power spectrum is computed revealing a periodic or nearly periodic component with a period of 568 +/- 10 days and a l/f(exp 3) power-law noise component in pulse phase with a noise strength S(sub infinity)=(1.24 +/- 0.067) x 10(exp 16) cycles(exp 2)/sec(exp 2) over the analysis frequency range f=0.003- 0.1 cycles/day. This result deviates from past analyses which characterized the pulse phase timing residuals as either l/f(sub 4) power-law noise or a quasiperiodic process. The analysis was checked using the Deeter polynomial method of power spectrum estimation that was developed for the case of nonuniform sampling, but has lower spectral resolution. The timing noise is consistent with a torque noise spectrum rising with analysis frequency as f implying blue torque noise, a result not predicted by current models of pulsar timing noise. If the periodic or nearly periodic component is due to a binary companion, we find a mass function f(M) = (6.8 +/- 2.4) x 10(exp -16) solar mass and a companion mass, M(sub c) is greater than or equal to 3.2 solar mass assuming a Crab pulsar mass of 1.4 solar mass.

Scott, D. M.↗
NASA NTRS2007

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

Interpolating scattered data points is a problem of wide ranging interest. A number of approaches for interpolation have been proposed both from theoretical domains such as computational geometry and in applications' fields such as geostatistics. Our motivation arises from geological and mining applications. In many instances data can be costly to compute and are available only at nonuniformly scattered positions. Because of the high cost of collecting measurements, high accuracy is required in the interpolants. One of the most popular interpolation methods in this field is called ordinary kriging. It is popular because it is a best linear unbiased estimator. The price for its statistical optimality is that the estimator is computationally very expensive. This is because the value of each interpolant is given by the solution of a large dense linear system. In practice, kriging problems have been solved approximately by restricting the domain to a small local neighborhood of points that lie near the query point. Determining the proper size for this neighborhood is a solved by ad hoc methods, and it has been shown that this approach leads to undesirable discontinuities in the interpolant. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. This process achieves its efficiency by replacing the large dense kriging system with a much sparser linear system. This technique has been applied to a restriction of our problem, called simple kriging, which is not unbiased for general data sets. In this paper we generalize these results by showing how to apply covariance tapering to the more general problem of ordinary kriging. Through experimentation we demonstrate the space and time efficiency and accuracy of approximating ordinary kriging through the use of covariance tapering combined with iterative methods for solving large sparse systems. We demonstrate our approach on large data sizes arising both from synthetic sources and from real applications.

Memarsadeghi, Nargess↗
NASA NTRS2020

Recommendations for Using Noise Monitors to Estimate Noise Exposure During X-59 Community Tests

A low fidelity simulation approach is used to explore how to place and use noise monitors during X-59 QueSST community tests, where people’s annoyance to the noise produced by the X-59 aircraft will be gathered. Several recommendations are provided including: 1) the desired number of sparsely spaced noise monitor sites within the survey area, 2) whether to group and average measurements across multiple noise monitors located at a site, 3) what spacing should be used if grouped noise monitors are used, 4) an approach to mitigate ambient noise contamination at the measurement sites, 5) a method to combine empirical and predicted dose estimates to provide a single dose estimate for respondents, and 6) assessing how changes in turbulence intensity and array configuration affect dose uncertainty. To make these recommendations, the error that is expected when fitting contrived, smoothly varying sonic boom “reference exposure surfaces” is studied when a spatially sparse and scattered set of samples is used as responses for the fit. The reference exposure surfaces mimic the sonic boom exposure at ground level that might be expected in the X-59 survey area in the absence of atmospheric turbulence, ambient noise, and other localized effects. The spatial extent of these surfaces varies and is representative of the different survey area sizes that might be expected during future X-59 community overflight tests. These contrived reference surfaces are sampled, and those reference samples are then perturbed to mimic atmospheric turbulence, ambient noise and other localized effects that might affect noise monitor measurements within overflown communities. Two different surface fitting methods are investigated when fitting these perturbed samples to approximate the reference surface. The first method uses interpolation between the perturbed data at the scattered sites to compute the fit. The second method fits a polynomial surface model to the perturbed data using ordinary least squares regression analysis. For both fitting methods, the root mean square fit error is computed from the pointwise difference between the fit surface and the reference surface as the count and configuration of the sites is varied while also averaging the error across many different realizations of both the smooth variation of the reference exposure surface and the random, localized perturbations at the sample sites. Different site configurations are compared using this error statistic to make the recommendations noted above. Additionally, the two fitting approaches (interpolation vs linear regression) are compared based on the fit error observed in these simulations. These analyses, comparisons, and recommendations should inform future decisions on the noise monitor placement and the methods used to analyze the noise monitor data that is collected during X-59 community overflights.

sonic boom↗
NASA NTRS1971

Determination of stratospheric temperature and height gradients from nimbus 3 radiation data

To improve the specification of stratospheric horizontal temperature and geopotential height fields from satellite radiation data, needed for high flying aircraft, a technique was derived to estimate data between satellite tracks using interpolated IRIS 15-micron data from Nimbus III. The interpolation is based on the observed gradients of the MRIR 15-micron radiances between subsatellite tracks. The technique was verified with radiosonde data taken within 6 hours of the satellite data. The sample varied from 1126 pairs at low levels to 383 pairs at 10 mb using northern hemisphere data for June 15 to July 20, 1969. The data were separated into five latitude bands. The Rms temperature differences were generally from 2 to 5 C for all levels above 300 mb. From 500 to 300 mb RMS differences vary from 4 to 9C except at high latitudes which show values near 3C. The RMS differences between radiosonde heights and those calculated hydrostatically from the surface were from 30 to 280 meters increasing from the surface to 10 mb. Integration starting at 100 mb reduced the RMS difference in the stratosphere to 20 to 120 meters from 70 to 10 mb. From a comparison with actual operational maps at 50 and 10 mb, it appears the techniques developed produce analyses in general agreement with those from radiosonde data. In addition, they are able to indicate details over areas of sparse data not shown by conventional techniques.

Nicholas, G. W.↗
NASA NTRS2011

Multiangle Implementation of Atmospheric Correction (MAIAC):: Radiative Transfer Basis and Look-up Tables - 1

This paper describes a radiative transfer basis of the algorithm MAIAC which performs simultaneous retrievals of atmospheric aerosol and bidirectional surface reflectance from the Moderate Resolution Imaging Spectroradiometer (MODIS). The retrievals are based on an accurate semianalytical solution for the top-of-atmosphere reflectance expressed as an explicit function of three parameters of the Ross-Thick Li-Sparse model of surface bidirectional reflectance. This solution depends on certain functions of atmospheric properties and geometry which are precomputed in the look-up table (LUT). This paper further considers correction of the LUT functions for variations of surface pressure/height and of atmospheric water vapor, which is a common task in the operational remote sensing. It introduces a new analytical method for the water vapor correction of the multiple ]scattering path radiance. It also summarizes the few basic principles that provide a high efficiency and accuracy of the LUT ]based radiative transfer for the aerosol/surface retrievals and optimize the size of LUT. For example, the single-scattering path radiance is calculated analytically for a given surface pressure and atmospheric water vapor. The same is true for the direct surface-reflected radiance, which along with the single-scattering path radiance largely defines the angular dependence of measurements. For these calculations, the aerosol phase functions and kernels of the surface bidirectional reflectance model are precalculated at a high angular resolution. The other radiative transfer functions depend rather smoothly on angles because of multiple scattering and can be calculated at coarser angular resolution to reduce the LUT size. At the same time, this resolution should be high enough to use the nearest neighbor geometry angles to avoid costly three ]dimensional interpolation. The pressure correction is implemented via linear interpolation between two LUTs computed for the standard and reduced pressure levels. A linear mixture and a modified linear mixture methods are used to represent different aerosol types in the aerosol/surface retrievals from several base models of the fine and coarse aerosol fractions. In summary, the developed LUT algorithm allows fast high-accuracy simulations of the outgoing radiance with full variability of the atmospheric and surface bidirectional reflectance properties for the aerosol/surface remote sensing.

Lyapustin, Alexei↗
NASA NTRS2021

Improved Rainfall Data in the Philippines through Concurrent Use of GPM IMERG and Ground-Based Measurements

The availability of accurate and reliable rainfall data that are applicable to various phenomenological, climatological, and modeling studies is important, especially in the Philippines, which is considered to be highly vulnerable to natural hazards and a changing climate. The presented strategy involved constructing a dataset consisting of synoptic data, automatic rain gauge (ARG) measurements, and satellite data that are co-registered, consistent, and formatted in the same manner. Although sparse in number, the synoptic stations provide the most accurate rainfall information and were used as the baseline for creating the dataset. The ARGs that are within a distance of 1 km to the synoptic stations were used to determine the correction factors needed to make the synoptic and ARG data consistent. Subsequently, the corrected ARGs were used to make the satellite IMERG data consistent with both ARG and synoptic data. In case of the latter, only IMERG pixels with at least 10 ARGs within the relatively large footprint of the satellite sensor were used in estimating the required correction parameters derived from a combination of a power transform and linear regression correction techniques. The final results show good agreement of synoptic and corrected ARG data with correlation coefficients of 0.94 and 0.97 for the 10 day and monthly data, respectively, and improvement in the linear regression slope from 0.67 to 0.90 for 10 day data, and 0.70 to 0.94 for monthly data. In addition, the corrected ARG data agree well with the corrected IMERG data, with correlation coefficients of 0.88 and 0.93 for the 10 day and monthly data, respectively, and an improvement in slope from 0.66 to 0.87 for 10 day data, and 0.74 to 0.99 for monthly data. The merit of using a combined dataset is illustrated through comparative analyses of the IMERG data and spatially interpolated synoptic and ARG data. The results show general agreements in spatial patterns of rainfall across the datasets, especially in areas where in situ measurements are recorded. The observed discrepancy when ground data is limited emphasizes the need for satellite IMERG data to obtain the true spatial patterns of rainfall distribution.

rainfall↗