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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Engineering Super–Poissonian Photon Statistics of Spatial Light Modes

The nature of light sources is defined by the statistical fluctuations of the electromagnetic field. As such, the photon statistics of light sources are typically associated with distinct emitters. Here, the possibility of producing light beams with various photon statistics through the spatial modulation of coherent light is demonstrated. This is achieved by the sequential encoding of controllable Kolmogorov phase screens in a digital micromirror device. Interestingly, the flexibility of this scheme allows for the shaping of spatial light modes with engineered photon statistics at different spatial positions. The performance of this scheme is assessed through the photon-number-resolving characterization of different families of spatial light modes with engineered photon statistics. Furthermore, it is believed that the possibility of controlling the photon fluctuations of the light field at arbitrary spatial locations has important implications for quantum spectroscopy, sensing, and imaging.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A novel statistical methodology for quantifying the spatial arrangements of axons in peripheral nerves

A thorough understanding of the neuroanatomy of peripheral nerves is required for a better insight into their function and the development of neuromodulation tools and strategies. In biophysical modeling, it is commonly assumed that the complex spatial arrangement of myelinated and unmyelinated axons in peripheral nerves is random, however, in reality the axonal organization is inhomogeneous and anisotropic. Present quantitative neuroanatomy methods analyze peripheral nerves in terms of the number of axons and the morphometric characteristics of the axons, such as area and diameter. In this study, we employed spatial statistics and point process models to describe the spatial arrangement of axons and Sinkhorn distances to compute the similarities between these arrangements (in terms of first- and second-order statistics) in various vagus and pelvic nerve cross-sections. We utilized high-resolution transmission electron microscopy (TEM) images that have been segmented using a custom-built high-throughput deep learning system based on a highly modified U-Net architecture. Our findings show a novel and innovative approach to quantifying similarities between spatial point patterns using metrics derived from the solution to the optimal transport problem. We also present a generalizable pipeline for quantitative analysis of peripheral nerve architecture. Our data demonstrate differences between male- and female-originating samples and similarities between the pelvic and abdominal vagus nerves.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1991

Homogeneity of spatial correlation statistics of tropical oceanic rainfall

The possibility of uniform horizontal correlation scales for tropical oceanic rainfall has been examined by a study of satellite-observed microwave data as a proxy measure of rain rates. From the brightness temperatures from the electrically scanning microwave radiometer on Nimbus 5 near nadir during the year 1974, the mean spatial autocorrelation function as a function of simultaneous pixel separation was calculated in each 5 by 5 deg grid box over the tropical Pacific and Atlantic for each season. The equal-time spatially lagged correlations were compared for geographical dependence to investigate the hypothesis of homogeneity. A simple model of the spatial statistics of the microwave brightness temperatures was used, consisting of a mixture of uncorrelated spatial white noise incoherently superimposed on a spatially correlated field (spatial red noise). The red noise signals are presumed to be generated by convective activity in the tropical atmosphere. The parameters of the red noise are consistent with this scheme over the tropical oceans, yielding a uniform spatial scale of about 50 km throughout.

Shin, Kyung-Sup↗
NASA NTRS2003

A Stochastic Model of Space-Time Variability of Mesoscale Rainfall: Statistics of Spatial Averages

A characteristic feature of rainfall statistics is that they depend on the space and time scales over which rain data are averaged. A previously developed spectral model of rain statistics that is designed to capture this property, predicts power law scaling behavior for the second moment statistics of area-averaged rain rate on the averaging length scale L as L right arrow 0. In the present work a more efficient method of estimating the model parameters is presented, and used to fit the model to the statistics of area-averaged rain rate derived from gridded radar precipitation data from TOGA COARE. Statistical properties of the data and the model predictions are compared over a wide range of averaging scales. An extension of the spectral model scaling relations to describe the dependence of the average fraction of grid boxes within an area containing nonzero rain (the "rainy area fraction") on the grid scale L is also explored.

Kundu, Prasun K.↗
DOE OSTI2023

Cluster characterization in atom probe tomography: Machine learning using multiple summary functions

In this work, we develop a machine learning-based method to characterize intracluster concentration (ρ c ), background concentration (ρ b ), clustering radius (r̄), and radius dispersity (δ r ) in simulated atom probe tomography data using multiple spatial statistics summary functions to train a Bayesian regularized neural network. Here, we build upon previous work that utilized Ripley’s K-function by incorporating additional features from nearest-neighbor spatial statistics summary functions to better characterize concentration-based metrics. The addition of nearest-neighbor based features allows for highly accurate estimates of ρ c and ρ b , both with 90% of the predictions within 4.0% of the real value; the root-mean-square errors are reduced by 81.5% and 92.8% from predictions using only K-function based features, respectively. Additionally, including these nearest-neighbor based features improves the ability to differentiate between r̄ and δ r .

36 MATERIALS SCIENCE↗
NASA NTRS2002

Scale Dependence of Statistics of Spatially Averaged Rain Rate Seen in TOGA COARE Comparison with Predictions from a Stochastic Model

A characteristic feature of rainfall statistics is that they in general depend on the space and time scales over which rain data are averaged. As a part of an earlier effort to determine the sampling error of satellite rain averages, a space-time model of rainfall statistics was developed to describe the statistics of gridded rain observed in GATE. The model allows one to compute the second moment statistics of space- and time-averaged rain rate which can be fitted to satellite or rain gauge data to determine the four model parameters appearing in the precipitation spectrum - an overall strength parameter, a characteristic length separating the long and short wavelength regimes and a characteristic relaxation time for decay of the autocorrelation of the instantaneous local rain rate and a certain 'fractal' power law exponent. For area-averaged instantaneous rain rate, this exponent governs the power law dependence of these statistics on the averaging length scale $L$ predicted by the model in the limit of small $L$. In particular, the variance of rain rate averaged over an $L \times L$ area exhibits a power law singularity as $L \rightarrow 0$. In the present work the model is used to investigate how the statistics of area-averaged rain rate over the tropical Western Pacific measured with ship borne radar during TOGA COARE (Tropical Ocean Global Atmosphere Coupled Ocean Atmospheric Response Experiment) and gridded on a 2 km grid depends on the size of the spatial averaging scale. Good agreement is found between the data and predictions from the model over a wide range of averaging length scales.

Kundu, Prasun K.↗
NASA NTRS1995

Measuring forest landscape patterns in the Cascade Range of Oregon, USA

This paper describes the use of a set of spatial statistics to quantify the landscape pattern caused by the patchwork of clearcuts made over a 15-year period in the western Cascades of Oregon. Fifteen areas were selected at random to represent a diversity of landscape fragmentation patterns. Managed forest stands (patches) were digitized and analyzed to produce both tabular and mapped information describing patch size, shape, abundance and spacing, and matrix characteristics of a given area. In addition, a GIS fragmentation index was developed which was found to be sensitive to patch abundance and to the spatial distribution of patches. Use of the GIS-derived index provides an automated method of determining the level of forest fragmentation and can be used to facilitate spatial analysis of the landscape for later coordination with field and remotely sensed data. A comparison of the spatial statistics calculated for the two years indicates an increase in forest fragmentation as characterized by an increase in mean patch abundance and a decrease in interpatch distance, amount of interior natural forest habitat, and the GIS fragmentation index. Such statistics capable of quantifying patch shape and spatial distribution may prove important in the evaluation of the changing character of interior and edge habitats for wildlife.

Ripple, William J.↗
NASA NTRS2018

Remote Sensing, Uncertainty Quantification, and a Theory of Data Systems; Workshop Report

The purpose of the workshop was to invite statisticians, applied mathematicians, computer scientists, data system architects, experts in remote sensing technology, and Climate and Earth System scientists to review, discuss, and plan research on issues related to large-scale, efficient analysis of distributed data using spatial statistical methods. Our motivation in organizing this event was to catalyze interchange among experts on the fast-emerging problem of analysis of distributed data. As part of SAMSI's 2017-2018 Program on Mathematical and Statistical Methods for Climate and the Earth System, a Working Group on Remote Sensing was established to address statistical and mathematical research problems in the analysis of remote sensing data. The Working Group has five subgroups: 1) Spatial Retrieval Methodology (the so-called \Spatial-X" subgroup); 2) Spatial Analysis for Hyperspectral Data (the so-called \Spatial-Y" subgroup); 3) Emulators for Complex Forward Models; 4) Optimization for Remote Sensing Retrievals; and 5) Theory of Data Systems (ToDS). The ToDS subgroup spent the first half of this academic year formulating a framework in which to consider the joint problem of a) optimizing statistical methods for environments where data are distributed and too large to move to a central location, and b) the design of data system infrastructures within which to implement those statistical methods. To x ideas, the Workshop focused on spatial statistical methods. To date there are many new spatial statistical methods designed with massive data sets in mind, in the literature. However, very few have been implemented for remote sensing data, and none have been implemented in operational settings like those used by NASA and NOAA. A major impediment to their use in these cases is that the data are not only massive, but are stored in different physical locations. These data must be brought together in some way in order to estimate spatial covariance functions, but moving data to a central location for analysis is tedious at best and impossible at worst. Some remote data reduction is almost certainly necessary, but how much? What are the consequences for inference? The fundamental issue underlying these questions is how to navigate the trade-space between costs and uncertainty in the estimates or inferences that are ultimately produced.

Braverman, Amy↗
NASA NTRS2002

A Stochastic Model of Space-Time Variability of Tropical Rainfall: I. Statistics of Spatial Averages

Global maps of rainfall are of great importance in connection with modeling of the earth s climate. Comparison between the maps of rainfall predicted by computer-generated climate models with observation provides a sensitive test for these models. To make such a comparison, one typically needs the total precipitation amount over a large area, which could be hundreds of kilometers in size over extended periods of time of order days or months. This presents a difficult problem since rain varies greatly from place to place as well as in time. Remote sensing methods using ground radar or satellites detect rain over a large area by essentially taking a series of snapshots at infrequent intervals and indirectly deriving the average rain intensity within a collection of pixels , usually several kilometers in size. They measure area average of rain at a particular instant. Rain gauges, on the other hand, record rain accumulation continuously in time but only over a very small area tens of centimeters across, say, the size of a dinner plate. They measure only a time average at a single location. In making use of either method one needs to fill in the gaps in the observation - either the gaps in the area covered or the gaps in time of observation. This involves using statistical models to obtain information about the rain that is missed from what is actually detected. This paper investigates such a statistical model and validates it with rain data collected over the tropical Western Pacific from ship borne radars during TOGA COARE (Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment). The model incorporates a number of commonly observed features of rain. While rain varies rapidly with location and time, the variability diminishes when averaged over larger areas or longer periods of time. Moreover, rain is patchy in nature - at any instant on the average only a certain fraction of the observed pixels contain rain. The fraction of area covered by rain decreases, as the size of a pixel becomes smaller. This means that within what looks like a patch of rainy area in a coarse resolution view with larger pixel size, one finds clusters of rainy and dry patches when viewed on a finer scale. The model makes definite predictions about how these and other related statistics depend on the pixel size. These predictions were found to agree well with data. In a subsequent second part of the work we plan to test the model with rain gauge data collected during the TRMM (Tropical Rainfall Measuring Mission) ground validation campaign.

Kundu, Prasun K.↗
DOE OSTI2022

Observation of spatter-induced stochastic lack-of-fusion in laser powder bed fusion using in situ process monitoring

Material produced via additive manufacturing (AM) continues to exhibit variable mechanical properties despite apparent optimization of processing parameters, inhibiting qualification efforts and limiting use in critical applications. Stochastic lack-of-fusion flaws may help explain this variability, but the origin of these seemingly random defects has to this point remained unclear. In this work, we show that spatter particles, material ejected from the laser melt pool, are directly responsible for generating stochastic lack-of-fusion in laser-based powder bed fusion components through the application of spatial statistics. Herein a statistically significant, causal relationship between spatter particles and stochastic lack-of-fusion is established, and the spatial and morphological relationships between spatter and internal flaws are investigated. The occurrence of spatter-induced lack-of-fusion in relation to the inert gas flow and laser trajectory direction is also investigated, and recommendations for mitigating the occurrence of spatter are evaluated.

36 MATERIALS SCIENCE↗
NASA NTRS2001

A Spatio-Temporal Approach for Global Validation and Analysis of MODIS Aerosol Products

With the launch of the MODIS sensor on the Terra spacecraft, new data sets of the global distribution and properties of aerosol are being retrieved, and need to be validated and analyzed. A system has been put in place to generate spatial statistics (mean, standard deviation, direction and rate of spatial variation, and spatial correlation coefficient) of the MODIS aerosol parameters over more than 100 validation sites spread around the globe. Corresponding statistics are also computed from temporal subsets of AERONET-derived aerosol data. The means and standard deviations of identical parameters from MOMS and AERONET are compared. Although, their means compare favorably, their standard deviations reveal some influence of surface effects on the MODIS aerosol retrievals over land, especially at low aerosol loading. The direction and rate of spatial variation from MODIS are used to study the spatial distribution of aerosols at various locations either individually or comparatively. This paper introduces the methodology for generating and analyzing the data sets used by the two MODIS aerosol validation papers in this issue.

Ichoku, Charles↗
DOE OSTI2025

Data-driven upper bounds and event attribution for unprecedented heatwaves

The last decade has seen numerous record-shattering heatwaves in all corners of the globe. In the aftermath of these devastating events, there is interest in identifying worst-case thresholds or upper bounds that quantify just how hot temperatures can become. Generalized Extreme Value theory provides a data-driven estimate of extreme thresholds; however, upper bounds may be exceeded by future events, which undermines attribution and planning for heatwave impacts. Here, we show how the occurrence and relative probability of observed yet unprecedented events that exceed a priori upper bound estimates, so-called “impossible” temperatures, has changed over time. We find that many unprecedented events are actually within data-driven upper bounds, but only when using modern spatial statistical methods. Furthermore, there are clear connections between anthropogenic forcing and the “impossibility” of the most extreme temperatures. Robust understanding of heatwave thresholds provides critical information about future record-breaking events and how their extremity relates to historical measurements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Influence of geometry on columnar to equiaxed transition during electron beam powder bed fusion of IN718

Correlation between spot-melt scan parameters (linear spot-density aka areal energy density), build geometry, and solidification microstructure evolution (columnar vs equiaxed) in a powder bed fusion technology is investigated. It is shown that to maintain the equiaxed solidification microstructure evolution in electron beam powder bed additive manufacturing (AM), the areal energy density per layer needs to be scaled with respect to the 2D cross-sectional area of the layer being melted. Samples with two different cross-sectional areas (40 × 40 mm and 20 × 20 mm) have been fabricated with varying areal energy densities. For a given square cross-section (20 × 20 mm), increasing the areal energy density (4.8 MJ/sq.m to 14.7 MJ/sq.m) transitioned the solidification microstructure from columnar to equiaxed. The observed microstructure data (Electron Back Scattered Diffraction - EBSD) is quantified by calculating the principal component (PC) score using a spatial statistics methodology. The sample with equiaxed grains is found to have a low PC score while the sample with columnar grain had a high PC score. A semi-analytical model is used to simulate the heat transfer and the local solidification conditions as a function of processing parameters (linear spot-density). The result from the heat transfer model is correlated with previously quantified microstructure data. Space-Time analysis of the melt pattern is done and correlated with the observed microstructure. In addition, from the findings, appropriate parameters have been used to additively manufacture a turbine blade with site-specific or hybrid solidification microstructure (traditional fabrication possible via a patented method of localized cold working and heat treatment).

36 MATERIALS SCIENCE↗
NASA NTRS2011

Multi-Sensor Aerosol Products Sampling System

Global and local properties of atmospheric aerosols have been extensively observed and measured using both spaceborne and ground-based instruments, especially during the last decade. Unique properties retrieved by the different instruments contribute to an unprecedented availability of the most complete set of complimentary aerosol measurements ever acquired. However, some of these measurements remain underutilized, largely due to the complexities involved in analyzing them synergistically. To characterize the inconsistencies and bridge the gap that exists between the sensors, we have established a Multi-sensor Aerosol Products Sampling System (MAPSS), which consistently samples and generates the spatial statistics (mean, standard deviation, direction and rate of spatial variation, and spatial correlation coefficient) of aerosol products from multiple spacebome sensors, including MODIS (on Terra and Aqua), MISR, OMI, POLDER, CALIOP, and SeaWiFS. Samples of satellite aerosol products are extracted over Aerosol Robotic Network (AERONET) locations as well as over other locations of interest such as those with available ground-based aerosol observations. In this way, MAPSS enables a direct cross-characterization and data integration between Level-2 aerosol observations from multiple sensors. In addition, the available well-characterized co-located ground-based data provides the basis for the integrated validation of these products. This paper explains the sampling methodology and concepts used in MAPSS, and demonstrates specific examples of using MAPSS for an integrated analysis of multiple aerosol products.

Petrenko, M.↗
DOE OSTI2025

Implementation of disruptive designs for gas turbine components using direct energy deposition additive manufacturing

This research aims to develop a framework for establishing the correlation between in-situ monitoring data, process parameters, and microstructure evolution in blown-powder laser-directed energy deposition (DED) additive manufacturing (AM). To achieve this, a comprehensive manufacturing framework has been developed, spanning from in-situ data acquisition, melt-pool simulation, microstructure modeling, and statistical microstructure quantification. A machine learning-based surrogate model is constructed to predict melt pool geometry directly from in-situ coaxial camera data. The surrogate model is trained using outputs from a high-fidelity melt pool simulation, which provides accurate melt pool dimension data under varying process conditions. The predicted melt pool geometry is then used as input to a microstructure model to predict microstructural features. To rigorously compare and analyze microstructures, the project introduces statistical metrics that quantify differences based on key features such as morphology and texture. Microstructures are represented using advanced statistical descriptors including angular chord length distribution, two-point spatial statistics, orientation distribution function, and global spherical harmonic. These representations are used to compute four distinct “dissimilarity scores” that quantitatively capture differences in texture and morphology. This framework is demonstrated to enable automated calibration of simulation parameters by minimizing discrepancies between simulated and target microstructures. The technology developed in this project enables direct correlation between in-situ monitoring data and resulting microstructure, paving the way for adaptive microstructure control in metal AM. This capability strengthens the connection between process parameters and final material properties, facilitating more precise and reliable material design.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Quantifying the influence of natural climate variability on in situ measurements of seasonal total and extreme daily precipitation

Abstract While various studies explore the relationship between individual sources of climate variability and extreme precipitation, there is a need for improved understanding of how these physical phenomena simultaneously influence precipitation in the observational record across the contiguous United States. In this work, we introduce a single framework for characterizing the historical signal (anthropogenic forcing) and noise (natural variability) in seasonal mean and extreme precipitation. An important aspect of our analysis is that we simultaneously isolate the individual effects of seven modes of variability while explicitly controlling for joint inter-mode relationships. Our method utilizes a spatial statistical component that uses in situ measurements to resolve relationships to their native scales; furthermore, we use a data-driven procedure to robustly determine statistical significance. In Part I of this work we focus on natural climate variability: detection is mostly limited to DJF and SON for the modes of variability considered, with the El Niño/Southern Oscillation, the Pacific–North American pattern, and the North Atlantic Oscillation exhibiting the largest influence. Across all climate indices considered, the signals are larger and can be detected more clearly for seasonal total versus extreme precipitation. We are able to detect at least some significant relationships in all seasons in spite of extremely large (> 95%) background variability in both mean and extreme precipitation. Furthermore, we specifically quantify how the spatial aspect of our analysis reduces uncertainty and increases detection of statistical significance while also discovering results that quantify the complex interconnected relationships between climate drivers and seasonal precipitation.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2005

Application of an Extended Parabolic Equation to the Calculation of the Mean Field and the Transverse and Longitudinal Mutual Coherence Functions Within Atmospheric Turbulence

Solutions are derived for the generalized mutual coherence function (MCF), i.e., the second order moment, of a random wave field propagating through a random medium within the context of the extended parabolic equation. Here, "generalized" connotes the consideration of both the transverse as well as the longitudinal second order moments (with respect to the direction of propagation). Such solutions will afford a comparison between the results of the parabolic equation within the pararaxial approximation and those of the wide-angle extended theory. To this end, a statistical operator method is developed which gives a general equation for an arbitrary spatial statistical moment of the wave field. The generality of the operator method allows one to obtain an expression for the second order field moment in the direction longitudinal to the direction of propagation. Analytical solutions to these equations are derived for the Kolmogorov and Tatarskii spectra of atmospheric permittivity fluctuations within the Markov approximation.

Manning, Robert M.↗