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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Geography of cretaceous extinctions: Data base development

Data bases built from the source literature are plagued by problems of data quality. Unless the data acquisition is done by experts, working slowly, the data base may contain so much garbage that true signals and patterns cannot be detected. On the other hand, high quality data bases develop so slowly that satisfactory statistical analysis may never be possible due to the small sample sizes. Results of a test are presented of the opposite strategy: rapid data acquisition by non-experts with minimal control on data quality. A published list of 186 species and genera of fossil invertibrates of the latest Cretaceous Age (Maestrichtian) were located through a random search of the paleobiological and geological literature. The geographic location for each faunal list was then transformed electronically to Maestrichtian latitude and longitude and the lists were further digested to identify the genera occurring in each ten-degree, latitude-longitude block. The geographical lists were clustered using the Otsuka similarity coefficient and a standard unweight-pair-group method. The resulting clusters are remarkably consistent geographically, indicating that a strong biogeographic signal is visible despite low-quality data. A further test evaluated the geographic pattern of end-Cretaceaous extinctions. All genera in the data base were compared with Sepkoski's compendium of time ranges of genera to determine which of the reported genera survived the Cretaceous mass extinction. In turn, extinction rates for the ten-degree, latitude-longitude blocks were mapped. The resulting distribution is readily interpretable as a robust pattern of the geography of the mass extinction. The study demonstrates that a low-quality data base, built rapidly, can provide a basis for meaningful analysis of past biotic events.

Raup, D. M.↗
NASA NTRS1993

Two generalizations of Kohonen clustering

The relationship between the sequential hard c-means (SHCM), learning vector quantization (LVQ), and fuzzy c-means (FCM) clustering algorithms is discussed. LVQ and SHCM suffer from several major problems. For example, they depend heavily on initialization. If the initial values of the cluster centers are outside the convex hull of the input data, such algorithms, even if they terminate, may not produce meaningful results in terms of prototypes for cluster representation. This is due in part to the fact that they update only the winning prototype for every input vector. The impact and interaction of these two families with Kohonen's self-organizing feature mapping (SOFM), which is not a clustering method, but which often leads ideas to clustering algorithms is discussed. Then two generalizations of LVQ that are explicitly designed as clustering algorithms are presented; these algorithms are referred to as generalized LVQ = GLVQ; and fuzzy LVQ = FLVQ. Learning rules are derived to optimize an objective function whose goal is to produce 'good clusters'. GLVQ/FLVQ (may) update every node in the clustering net for each input vector. Neither GLVQ nor FLVQ depends upon a choice for the update neighborhood or learning rate distribution - these are taken care of automatically. Segmentation of a gray tone image is used as a typical application of these algorithms to illustrate the performance of GLVQ/FLVQ.

Bezdek, James C.↗
NASA NTRS1985

Rotation and flattening of globular clusters

Methods for measuring globular cluster ellipticities and the results of such measurements are reviewed, and the processes that determine the shapes of globular clusters and the ways in which they change with time are discussed. The use of the virial tensor theorem to study the connection between the global rotation, velocity anisotropy, and the shape of a self-gravitating system is addressed, and the employment of N-body models to simulate the evolution of globular clusters with initially anisotropic velocity distributions is examined. The application of a simple evaporation model and Fokker-Planck integrations to study the two-body diffusion in globular clusters is reviewed.

Fall, S. M.↗
NASA NTRS2015

Reconstructing Emission from Pre-Reionization Sources with Cosmic Infrared Background Fluctuation Measurements by the JWST

We present new methodology to use cosmic infrared background (CIB) fluctuations to probe sources at 10 less than or approx. equal to z less than or approx. equal to 30 from a James Webb Space Telescope (JWST) NIRCam configuration that will isolate known galaxies to 28 AB mag at 0.55 m. At present significant mutually consistent source-subtracted CIB fluctuations have been identified in the Spitzer and AKARI data at 25 m, but we demonstrate internal inconsistencies at shorter wavelengths in the recent CIBER data. We evaluate CIB contributions from remaining galaxies and show that the bulk of the high-z sources will be in the confusion noise of the NIRCam beam, requiring CIB studies. The accurate measurement of the angular spectrum of the fluctuations and probing the dependence of its clustering component on the remaining shot noise power would discriminate between the various currently proposed models for their origin and probe the flux distribution of its sources. We show that the contribution to CIB fluctuations from remaining galaxies is large at visible wavelengths for the current instruments precluding probing the putative Lyman-break of the CIB fluctuations. We demonstrate that with the proposed JWST configuration such measurements will enable probing the Lyman-break. We develop a Lyman-break tomography method to use the NIRCam wavelength coverage to identify or constrain, via the adjacent two-band subtraction, the history of emissions over 10 less than or approx. equal to z less than or approx. equal to 30 as the universe comes out of the Dark Ages. We apply the proposed tomography to the current SpitzerIRAC measurements at 3.6 and 4.5 m, to find that it already leads to interestingly low upper limit on emissions at z greater than or approx. equal to 30.

NIRCam beam↗
NASA NTRS2003

Formation and Evolution of Binary Systems Containing Collapsed Stars

This research includes theoretical studies of the formation and evolution of five types of interacting binary systems. Our main focus has been on developing a number of comprehensive population synthesis codes to study the following types of binary systems: (i) cataclysmic variables (#3, #8, #12, #15), (ii) low- and intermediate-mass X-ray binaries (#13, #20, #21), (iii) high-mass X-ray binaries (#14, #17, #22), (iv) recycled binary millisecond pulsars in globular clusters (#5, #10, #ll), and (v) planetary nebulae which form in interacting binaries (#6, #9). The numbers in parentheses refer to papers published or in preparation that are listed in this paper. These codes take a new unified approach to population synthesis studies. The first step involves a Monte Carlo selection of the primordial binaries, including the constituent masses, and orbital separations and eccentricities. Next, a variety of analytic methods are used to evolve the primary star to the point where either a dynamical episode of mass transfer to the secondary occurs (the common envelope phase), or the system evolves down an alternate path. If the residual core of the primary is greater than 2.5 solar mass, it will evolve to Fe core collapse and the production of a neutron star and a supernova explosion. In the case of systems involving neutron stars, a kick velocity is chosen randomly from an appropriate distribution and added to the orbital dynamics which determine the state of the binary system after the supernova explosion. In the third step, all binaries which commence stable mass transfer from the donor star (the original secondary in the binary system) to the compact object, are followed with a detailed binary evolution code. Finally, we include all the relevant dynamics of the binary system. For example, in the case of LMXBs, the binary system, with its recoil velocity from the supernova explosion, is followed in time through its path in the Galactic potential. For our globular cluster study, detailed three-body calculations are used to follow the interactions of the binary with passing field stars.

Rappaport, Saul↗
NASA NTRS2009

Spherical Harmonic Analysis of Particle Velocity Distribution Function: Comparison of Moments and Anisotropies using Cluster Data

This paper presents a spherical harmonic analysis of the plasma velocity distribution function using high-angular, energy, and time resolution Cluster data obtained from the PEACE spectrometer instrument to demonstrate how this analysis models the particle distribution function and its moments and anisotropies. The results show that spherical harmonic analysis produced a robust physical representation model of the velocity distribution function, resolving the main features of the measured distributions. From the spherical harmonic analysis, a minimum set of nine spectral coefficients was obtained from which the moment (up to the heat flux), anisotropy, and asymmetry calculations of the velocity distribution function were obtained. The spherical harmonic method provides a potentially effective "compression" technique that can be easily carried out onboard a spacecraft to determine the moments and anisotropies of the particle velocity distribution function for any species. These calculations were implemented using three different approaches, namely, the standard traditional integration, the spherical harmonic (SPH) spectral coefficients integration, and the singular value decomposition (SVD) on the spherical harmonic methods. A comparison among the various methods shows that both SPH and SVD approaches provide remarkable agreement with the standard moment integration method.

Gurgiolo, Chris↗
NASA NTRS2006

A New Spin for Understanding the Peculiar Horizontal Branch Morphology of the Galactic Globular Clusters NGC 6388 and NGC 6441

In this paper we present multiband optical and UV Hubble Space Telescope photometry of the two Galactic globular clusters NGC 6388 and NGC 6441 Aims. We investigate the properties of their anomalous horizontal branches (HB) in different photometric planes in order to shed light on the nature of the physical mechanism(s) responsible for the existence of an extended HB blue tail, and of a slope in the HB, visible in all the color-magnitude diagrams. Methods. New photometric data have been collected and carefully reduced. Empirical data have been compared with updated stellar models of low-mass, metal-rich, He-burning structures, transformed to the observational plane with appropriate atmosphere models. Results. We have obtained the first UV color-magnitude diagrams for NGC 6388 and NGC 6441. These diagrams confirm previous results, obtained in optical bands, about the presence of a sizeable stellar population of extremely hot Horizontal Branch stars. At least in NGC 6388, we find a clear indication that at the hot end of the horizontal branch the distribution of stars forms a hook-like feature, closely resembling those observed in NGC 2808 and w Centauri. We briefly review the theoretical scenarios which have been suggested for interpreting this observational feature. We investigate also on the tilt in the horizontal branch morphology, and provide further evidence that supports early suggestions according to which this feature cannot be interpreted as an effect of differential reddening or radiative levitation, though these effects contribute to create the anomaly. We demonstrate that a possible solution of the puzzle is to assume that a small fraction (approx. 13% in NGC 6388 and approx. 8% NGC 6441) of the stellar population in the two clusters is strongly helium enriched (Y approx. 0.40 in NGC6388 and Y approx. 0.35 in NGC 6441). This solution necessarily implies the presence of a double generation of stars in the two clusters.

Busso, G.↗
NASA NTRS2005

Identification of a typical flight patterns

Method and system for analyzing aircraft data, including multiple selected flight parameters for a selected phase of a selected flight, and for determining when the selected phase of the selected flight is atypical, when compared with corresponding data for the same phase for other similar flights. A flight signature is computed using continuous- valued and discrete-valued flight parameters for the selected flight parameters and is optionally compared with a statistical distribution of other observed flight signatures, yielding a typicality scores for the same phase for other similar flights. A cluster analysis is optionally applied to the flight signatures to define an optimal collection of clusters. A level of atypicality for a selected flight is estimated, based upon an index associated with the cluster analysis.

Irving C Statler↗
NASA NTRS2005

Identification of atypical flight patterns

Method and system for analyzing aircraft data, including multiple selected flight parameters for a selected phase of a selected flight, and for determining when the selected phase of the selected flight is atypical, when compared with corresponding data for the same phase for other similar flights. A flight signature is computed using continuous-valued and discrete-valued flight parameters for the selected flight parameters and is optionally compared with a statistical distribution of other observed flight signatures, yielding atypicality scores for the same phase for other similar flights. A cluster analysis is optionally applied to the flight signatures to define an optimal collection of clusters. A level of atypicality for a selected flight is estimated, based upon an index associated with the cluster analysis.

Statler, Irving C.↗
NASA NTRS2007

A Catalog of Galaxy Clusters Observed by XMM-Newton

Images and the radial profiles of the temperature, abundance, and brightness for 70 clusters of galaxies observed by XMM-Newton are presented along with a detailed discussion of the data reduction and analysis methods, including background modeling, which were used in the processing. Proper consideration of the various background components is vital to extend the reliable determination of cluster parameters to the largest possible cluster radii. The various components of the background including the quiescent particle background, cosmic diffuse emission, soft proton contamination, and solar wind charge exchange emission are discussed along with suggested means of their identification, filtering, and/or their modeling and subtraction. Every component is spectrally variable, sometimes significantly so, and all components except the cosmic background are temporally variable as well. The distributions of the events over the FOV vary between the components, and some distributions vary with energy. The scientific results from observations of low surface brightness objects and the diffuse background itself can be strongly affected by these background components and therefore great care should be taken in their consideration.

Snowden, S. L.↗
NASA NTRS2003

Review of Laser Ablation Process for Single Wall Carbon Nanotube Production

Different types of lasers are now routinely used to prepare single wall carbon nanotubes (SWCNTs). The original method developed by researchers at Rice University utilized a "double pulse laser oven" process. A graphite target containing about 1 atomic percent of metal catalysts is ablated inside a 1473K oven using laser pulses (10 ns pulse width) in slow flowing argon. Two YAG lasers with a green pulse (532 nm) followed by an IR pulse (1064 nm) with a 50 ns delay are used for ablation. This set up produced single wall carbon nanotube material with about 70% purity having a diameter distribution peaked around 1.4 nm. The impurities consist of fullerenes, metal catalyst clusters (10 to 100 nm diameter) and amorphous carbon. The rate of production with the initial set up was about 60 mg per hour with 10Hz laser systems. Several researchers have used variations of the lasers to improve the rate, consistency and study effects of different process parameters on the quality and quantity of SWCNTs. These variations include one to three YAG laser systems (Green, Green and IR), different pulse widths (nano to microseconds as well as continuous) and different laser wavelengths (Alexandrite, CO, CO2, free electron lasers in the near to far infrared). It is noted that yield from the single laser (Green or IR) systems is only a fraction of the two laser systems. The yield seemed to scale up with the repetition rate of the laser systems (10 to 60 Hz) and depended on the beam uniformity and quality of the laser pulses. The shift to longer wavelength lasers (free electron, CO and CO2) did not improve the quality, but increased the rate of production because these lasers are either continuous (CW) or high repetition rate pulses (kHz to MHz). The average power and the peak power of the lasers seem to influence the yields. Very high peak powers (MegaWatts per square centimeter) are noted to increase ablation of bigger particles with reduced yields of SWCNTs. Increased average powers seem to help the conversion of the carbon from target into vapor phase to improve formation of nanotubes. The use of CW far infrared lasers reduced the need for the oven, at the expense of controlled ablation. Some of these variations are tried with different combinations and concentrations of metal catalysts (Nickel with Cobalt, Iron, Palladium and Platinum) different buffer gases (e.g. Helium); with different oven temperatures (Room temperature to 1473K); under different flow conditions (1 to 1000 kPa) and even different porosities of the graphite targets. It is to be noted that the original Cobalt and Nickel combination worked best, possibly because of improved carbonization with stable crystalline phases. The mean diameter and yield seemed to increase with increasing oven temperatures. Thermal conductivity of the buffer gas and flow conditions dictate the quality as well as quantity of the SWCNTs. Faster flows, lower pressures and heavier gases seem to increase the yields. This review will attempt to cover all these variations and their relative merits. Possible growth mechanisms under these different conditions will also be discussed.

Arepalli, Sivaram↗
NASA NTRS2022

Superclustering with the Atacama Cosmology Telescope and Dark Energy Survey. I. Evidence for Thermal Energy Anisotropy Using Oriented Stacking

The cosmic web contains filamentary structure on a wide range of scales. On the largest scales, superclustering aligns multiple galaxy clusters along intercluster bridges, visible through their thermal Sunyaev–Zel'dovich signal in the cosmic microwave background. We demonstrate a new, flexible method to analyze the hot gas signal from multiscale extended structures. We use a Compton y-map from the Atacama Cosmology Telescope (ACT) stacked on redMaPPer cluster positions from the optical Dark Energy Survey (DES). Cutout images from the y-map are oriented with large-scale structure information from DES galaxy data such that the superclustering signal is aligned before being overlaid. We find evidence of an extended quadrupole moment of the stacked y signal at the 3.5σ level, demonstrating that the large-scale thermal energy surrounding galaxy clusters is anisotropically distributed. We compare our ACT × DES results with the Buzzard simulations, finding broad agreement. Using simulations, we highlight the promise of this novel technique for constraining the evolution of anisotropic, non-Gaussian structure using future combinations of microwave and optical surveys.

M. Lokken↗
NASA NTRS2023

Far-Infrared Line Emission from the Outer Galaxy Cluster Gy 3–7 With SOFIA/FIFI-LS: Physical Conditions and UV Fields

Context. Far-infrared (FIR) line emission provides key information about the gas cooling and heating due to shocks and UV radiation associated with the early stages of star formation. Gas cooling via FIR lines might, however, depend on metallicity. Aims. We aim to quantify the FIR line emission and determine the spatial distribution of the CO rotational temperature, ultraviolet (UV) radiation field, and H2 number density toward the embedded cluster Gy 3–7 in the CMa–l224 star-forming region, whose metallicity is expected to be intermediate between that of the Large Magellanic Cloud and the Solar neighborhood. By comparing the total luminosities of CO and [O I] toward Gy 3–7 with values found for low- and high-mass protostars extending over a broad range of metallicities, we also aim to identify the possible effects of metallicity on the FIR line cooling within our Galaxy. Methods. We studied SOFIA/FIFI-LS spectra of Gy 3–7, covering several CO transitions from J = 14–13 to 31-30, the OH doublet at 79 µm, the [O I] 63.2 and 145.5 µm, and the [C II] 158 µm lines. The field of view covers a 2 0 × 1 0 region with a resolution of ∼7 00–1800 . Results. The spatial extent of CO high-J (Jup ≥14) emission resembles that of the elongated 160 µm continuum emission detected with Herschel, but its peaks are offset from the positions of the dense cores. The [O I] lines at 63.2 µm and 145.5 µm follow a similar pattern, but their peaks are found closer to the positions of the cores. The CO transitions from J = 14–13 to J = 16–15 are detected throughout the cluster and show a median rotational temperature of 170 ± 30 K on Boltzmann diagrams. Comparisons to other protostars observed with Herschel show a good agreement with intermediate-mass sources in the inner Galaxy. Assuming an origin of the [O I] and high-J CO emission in UV-irradiated C−shocks, we obtained pre-shock H2 number densities of 104–105 cm−3 and UV radiation field strengths of 0.1–10 Habing fields (G0). Conclusions. Far-IR line observations reveal ongoing star formation in Gy 3–7, dominated by intermediate-mass Class 0/I young stellar objects. The ratio of molecular-to-atomic far-IR line emission shows a decreasing trend with bolometric luminosities of the protostars. However, it does not indicate that the low-metallicity has an impact on the line cooling in Gy 3–7.

stars: formation↗
NASA NTRS1976

Encounters of spherical galaxies. I - Galaxy models with one stellar population. II - Galaxy models with two stellar populations

Close encounters between two spherical galaxies of equal size and consisting of only one stellar population are calculated using models of elliptical galaxies constructed according to King's (1966) method. The mass loss and the change in internal energy are computed under the assumption that the stars do not change their velocity or density distributions during the encounters. The results for a specific case are compared with the calculations of Gallagher and Ostriker (1972), who employed the observed brightness distribution and the derived density distribution of the E1 galaxy NGC 3379. For models with one stellar population, the results suggest that the radius of a galactic halo would have to be at least 200 kpc for appreciable mass loss to occur over the history of a galaxy in a rich cluster. The calculations are then extended to include a halo population characterized by a high central velocity dispersion. In this case, it is found that the halo population of sufficiently large galaxies can be dispersed without appreciably affecting the main population. It is suggested that the missing mass of many clusters of galaxies may be located in an intergalactic sea of faint stars making up an envelope for the centrally located gE galaxies.

Biermann, P.↗
NASA NTRS2019

Application of High-Dimensional Fuzzy K-Means Cluster Analysis to CALIOP/CALIPSO Version 4.1 Cloud-Aerosol Discrimination

This study applies fuzzy k-means (FKM) cluster analyses to a subset of the parameters reported in the CALIPSO lidar level 2 data products in order to classify the layers detected as either clouds or aerosols. The results obtained are used to assess the reliability of the cloud–aerosol discrimination (CAD) scores reported in the version 4.1 release of the CALIPSO data products. FKM is an unsupervised learning algorithm, whereas the CALIPSO operational CAD algorithm (COCA) takes a highly supervised approach. Despite these substantial computational and architectural differences, our statistical analyses show that the FKM classifications agree with the COCA classifications for more than 94 % of the cases in the troposphere. This high degree of similarity is achieved because the lidar-measured signatures of the majority of the clouds and the aerosols are naturally distinct, and hence objective methods can independently and effectively separate the two classes in most cases. Classification differences most often occur in complex scenes (e.g., evaporating water cloud filaments embedded in dense aerosol) or when observing diffuse features that occur only intermittently (e.g., volcanic ash in the tropical tropopause layer). The two methods examined in this study establish overall classification correctness boundaries due to their differing algorithm uncertainties. In addition to comparing the outputs from the two algorithms, analysis of sampling, data training, performance measurements, fuzzy linear discriminants, defuzzification, error propagation, and key parameters in feature type discrimination with the FKM method are further discussed in order to better understand the utility and limits of the application of clustering algorithms to space lidar measurements. In general, we find that both FKM and COCA classification uncertainties are only minimally affected by noise in the CALIPSO measurements, though both algorithms can be challenged by especially complex scenes containing mixtures of discrete layer types. Our analysis results show that attenuated backscatter and color ratio are the driving factors that separate water clouds from aerosols; backscatter intensity, depolarization, and mid-layer altitude are most useful in discriminating between aerosols and ice clouds; and the joint distribution of backscatter intensity and depolarization ratio is critically important for distinguishing ice clouds from water clouds.

Zeng, Shan↗
NASA NTRS1992

Sea surface velocities from visible and infrared multispectral atmospheric mapping sensor imagery

High resolution (100 m), sequential Multispectral Atmospheric Mapping Sensor (MAMS) images were used in a study to calculate advective surface velocities using the Maximum Cross Correlation (MCC) technique. Radiance and brightness temperature gradient magnitude images were formed from visible (0.48 microns) and infrared (11.12 microns) image pairs, respectively, of Chandeleur Sound, which is a shallow body of water northeast of the Mississippi delta, at 145546 GMT and 170701 GMT on 30 Mar. 1989. The gradient magnitude images enhanced the surface water feature boundaries, and a lower cutoff on the gradient magnitudes calculated allowed the undesirable sunglare and backscatter gradients in the visible images, and the water vapor absorption gradients in the infrared images, to be reduced in strength. Requiring high (greater than 0.4) maximum cross correlation coefficients and spatial coherence of the vector field aided in the selection of an optimal template size of 10 x 10 pixels (first image) and search limit of 20 pixels (second image) to use in the MCC technique. Use of these optimum input parameters to the MCC algorithm, and high correlation and spatial coherence filtering of the resulting velocity field from the MCC calculation yielded a clustered velocity distribution over the visible and infrared gradient images. The velocity field calculated from the visible gradient image pair agreed well with a subjective analysis of the motion, but the velocity field from the infrared gradient image pair did not. This was attributed to the changing shapes of the gradient features, their nonuniqueness, and large displacements relative to the mean distance between them. These problems implied a lower repeat time for the imagery was needed in order to improve the velocity field derived from gradient imagery. Suggestions are given for optimizing the repeat time of sequential imagery when using the MCC method for motion studies. Applying the MCC method to the infrared brightness temperature imagery yielded a velocity field which did agree with the subjective analysis of the motion and that derived from the visible gradient imagery. Differences between the visible and infrared derived velocities were 14.9 cm/s in speed and 56.7 degrees in direction. Both of these velocity fields also agreed well with the motion expected from considerations of the ocean bottom topography and wind and tidal forcing in the study area during the 2.175 hour time interval.

Pope, P. A.↗
NASA NTRS1994

Two-fluid simulations of galaxy formation

We investigate the formation of galaxies and larger structure with a simulation modeling two gravitationally coupled fluids representing dark matter and baryons. The baryon gas dynamics are calculated with a smoothed particle hydrodynamics (SPH) method, and the physics modeled includes thermal pressure, shock heating, and radiative cooling. We simulate a 16 Mpc periodic cube with 64(exp 3) particles in each fluid and 10% baryon mass fraction. We confirm, for the first time experimentally, disk formation as a natural consequence of hierarchical clustering in a large-scale cosmological environment. The majority of isolated galaxies exhibit centrifugally supported disks. A power-law relation between cold baryonic mass and maximum rotation velocity is found, M varies as nu(sub rot)(exp alpha) with alpha = 2.5 after correcting for differential numerical resolution. Both the spatial and velocity distributions of the simulated galaxies are biased with respect to the dark matter. A counts-in-cells analysis indicates that an unphysical degree of merging in the central cluster is likely responsible for the antibias signal in the correlation function. A robust, scale-dependent velocity bias is measured. The ratio of galaxy to dark matter pairwise velocity dispersions on a scale of 1 Mpc is 0.7. The amplitude is only mildly dependent on redshift or mass cutoff and scales with separation as r(exp 0.2). The degree to which these results depend on numerical parameters is discussed. Mass resolution plays a key role in controlling the resulting fraction of cold, dense baryons. The mass fraction associated with galaxies decreases by a factor of approximately greater than 3 when the mass per particle is increased by a factor 8. Photoionization and energy input from supernova will have to be included to determine more carefully the fraction of highly dissipated material and the characteristics of the stellar component of galaxies.

Evrard, August E.↗
NASA NTRS2019

Lightning Strike Distance Distribution Beyond a Preexisting Lightning Area

The 45th Weather Squadron (45 WS) asked the Applied Meteorology Unit (AMU) to review the 30-year-old, lightning stand-off distances of 5 nautical miles (nmi) for applicability to today's operations. This was based on the realization that previous lightning strike distance studies did not match how 45 WS issues lightning warnings (Roeder, 2008). The previous lightning distance studies were from the point of origin of the lightning or the average starting location that would tend to be in the core of the thunderstorm. However, the 45 WS issues lightning warnings based on the edge of a preexisting lightning area. Before beginning the AMU project, it took several years to develop a method to calculate a distance distribution beyond a preexisting area (Roeder, 2015). The AMU pulled Lightning Detection and Ranging (LDAR) sensor data from 1/1/2013 to 12/31/2013. This dataset consisted of 37 million individual source data points from the LDAR sensors. Only sources within 50 km north, south, east or west of the LDAR grid center were included in the dataset. This limited the use of LDAR data to that with the greatest accuracy of source detection and increased data processing. Points were grouped into flashes based on spatial and temporal criteria. Based on the sensitivity analysis the AMU performed on the flash clustering algorithm, a time value of 0.3 seconds was found to model flashes adequately. Distance parameters were tested from 1,500 to 7,500 meters (m) in 500 m increments. Distance parameters of both 3,000 m and 4,000 m produced results in the plotting tool that were most representative of the physical behavior of lightning. Thus statistics were gathered for the most representative of these spatial and temporal criteria on the flash size and the polygon expansion distance in order to find the correct data distributions. The best fit curves for the LDAR polygon expansion frequency vs. distances for both the 3 kilometer (km) and 4 km distance threshold values were exponential decay functions and had R2 values of > 0.998, indicating good model fits. The equations of the best fit curves were then used to calculate a desired safety radius of 4 nmi for either 3 km or 4 km distance threshold criteria. The AMU analysis concludes the safe reduction of the 5 nmi lightning warning circles to 4 nmi should improve the operational impact by 36% if based on distance from the center of the property area being protected. If based on the edge of the property being protected, then the reduction is 4.5 nmi to 4 nmi and the operational impact is decreased by 21%. For the 6 nmi lightning warning circles, the recommended 4 nmi stand-off distance will result in a safe reduction of operational impact of 31% if based on the center of the area being protected, or 16% if based on the edge of the property.

Flash clustering algorithm↗