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At least 991 records · Page 55

Method for Balancing Detector Output to a Desired Level of Balance at a Frequency

A multi-gas sensor is provided which modulates a polarized light beam over a broadband of wavelengths between two alternating orthogonal polarization components. The two orthogonal polarization components of the polarization modulated beam are directed along two distinct optical paths. At least one optical path contains one or more spectral discrimination elements, with each spectral discrimination element having spectral absorption features of one or more gases of interest being measured. The two optical paths then intersect, and one orthogonal component of the intersected components is transmitted and the other orthogonal component is reflected. The combined polarization modulated beam is partitioned into one or more smaller spectral regions of interest where one or more gases of interest has an absorption band. The difference in intensity between the two orthogonal polarization components is then determined in each partitioned spectral region of interest as an indication of the spectral emission/absorption of the light beam by the gases of interest in the measurement path. The spectral emission/absorption is indicative of the concentration of the one or more gases of interest in the measurement path. More specifically, one embodiment of the present invention is a gas filter correlation radiometer which comprises a polarizer, a polarization modulator, a polarization beam splitter, a beam combiner, wavelength partitioning element, and detection element. The gases of interest are measured simultaneously and, further, can be measured independently or non-independently. Furthermore, optical or electronic element are provided to balance optical intensities between the two optical paths.

Sachse, Glenn W.↗

Use of Atomic Oxygen for the Determination of Document Alteration

Atomic oxygen, which normally is found only the near Earth space environment, causes oxidation and erosion of polymers on spacecraft. The development of technology to prevent this degradation has required NASA to develop ground laboratory facilities that generate atomic oxygen. Atomic oxygen has also been found to be able to oxidize most types of ink from a variety of types of pens. The use of atomic oxygen to identify alteration of documents has been investigated and is reported. Results of testing indicates that for many types of ink, pen, and paper, identification of document alteration of pen and ink numbers and evidence of alteration can be made visible by exposing the questionable writing to atomic oxygen. Atomic oxygen provides discrimination because different inks may oxidize at different rates, the amount of time between delayed alteration may add to ink thickness at crossings, and the end of pen strokes tend to have much thicker ink deposits than the rest of the character. Examples and techniques of using atomic oxygen to identify document alteration indicate that the technology can, in many but not all cases, provide discrimination between original and altered documents.

Banks, Bruce A.↗

Foliar Reflectance and Fluorescence Responses for Plants Under Nitrogen Stress Determined with Active and Passive Systems

Vegetation productivity is driven by nitrogen (N) availability in soils. Both excessive and low soil N induce physiological changes in plant foliage. In 2001, we examined the use of spectral fluorescence and reflectance measurements to discriminate among plants provided different N fertilizer application rates: 20%, 50%, 100% and 150% of optimal N levels. A suite of optical, fluorescence, and biophysical measurements were collected on leaves from field grown corn (Zea mays L.) and soybean plants (Glycine max L.) grown in pots (greenhouse + ambient sunlight daily). Three types of steady state laser-induced fluorescence measurements were made on adaxial and abaxial surfaces: 1) fluorescence images in four 10 nm bands (blue, green, red, far-red) resulting from broad irradiance excitation; 2) emission spectra (5 nm resolution) produced by excitation at single wavelengths (280,380 or 360, and 532 nm); and 3) excitation spectra (2 nm resolution), with emission wavelengths fixed at wavelengths centered on selected solar Fraunhofer lines (532,607,677 and 745 nm). Two complementary sets of high resolution (less than 2 nm) optical spectra were acquired for both adaxial and abaxial leaf surfaces: 1) optical properties (350-2500 nm) for reflectance, transmittance, and absorptance; and 2) reflectance spectra (500-1000 nm) acquired with and without a short pass filter at 665 nm to determine the fluorescence contribution to apparent reflectance in the 650-750 spectrum, especially at the 685 and 740 nm chlorophyll fluorescence (ChIF) peaks. The strongest relationships between foliar chemistry and optical properties were demonstrated for C/N content and two optical parameters associated with the red edge inflection point. Select optical properties and ChIF parameters were highly correlated for both species. A significant contribution of ChIF to apparent reflectance was observed, averaging 10-25% at 685 nm and 2 - 6% at 740 nm over all N treatments. Discrimination of N treatment groups was possible with specific fluorescence band ratios (e.g., F740/F525 obtained with 380EX). From all measurements assessing fluorescence, higher ChIF and blue/green emissions were measured from the abaxial leaf surfaces; Abaxial surfaces also produced higher reflectances in the 400-800 nm spectrum. Fluorescence information collected in Fraunhofer regions located on the shoulders of ChIF features compared favorably with peak emissions. This supports the potential capability of a future space-born interferometer sensor to capture plant canopy fluorescence.

Middleton, E. M.↗

Virtual Sensors: Using Data Mining to Efficiently Estimate Spectra

Detecting clouds within a satellite image is essential for retrieving surface geophysical parameters, such as albedo and temperature, from optical and thermal imagery because the retrieval methods tend to be valid for clear skies only. Thus, routine satellite data processing requires reliable automated cloud detection algorithms that are applicable to many surface types. Unfortunately, cloud detection over snow and ice is difficult due to the lack of spectral contrast between clouds and snow. Snow and clouds are both highly reflective in the visible wavelen,ats and often show little contrast in the thermal Infrared. However, at 1.6 microns, the spectral signatures of snow and clouds differ enough to allow improved snow/ice/cloud discrimination. The recent Terra and Aqua Moderate Resolution Imaging Spectro-Radiometer (MODIS) sensors have a channel (channel 6) at 1.6 microns. Presently the most comprehensive, long-term information on surface albedo and temperature over snow- and ice-covered surfaces comes from the Advanced Very High Resolution Radiometer ( AVHRR) sensor that has been providing imagery since July 1981. The earlier AVHRR sensors (e.g. AVHRR/2) did not however have a channel designed for discriminating clouds from snow, such as the 1.6 micron channel available on the more recent AVHRR/3 or the MODIS sensors. In the absence of the 1.6 micron channel, the AVHRR Polar Pathfinder (APP) product performs cloud detection using a combination of time-series analysis and multispectral threshold tests based on the satellite's measuring channels to produce a cloud mask. The method has been found to work reasonably well over sea ice, but not so well over the ice sheets. Thus, improving the cloud mask in the APP dataset would be extremely helpful toward increasing the accuracy of the albedo and temperature retrievals, as well as extending the time-series of albedo and temperature retrievals from the more recent sensors to the historical ones. In this work, we use data mining methods to construct a model of MODIS channel 6 as a function of other channels that are common to both MODIS and AVHRR. The idea is to use the model to generate the equivalent of MODIS channel 6 for AVHRR as a function of the AVHRR equivalents to MODIS channels. We call this a Virtual Sensor because it predicts unmeasured spectra. The goal is to use this virtual channel 6. to yield a cloud mask superior to what is currently used in APP . Our results show that several data mining methods such as multilayer perceptrons (MLPs), ensemble methods (e.g., bagging), and kernel methods (e.g., support vector machines) generate channel 6 for unseen MODIS images with high accuracy. Because the true channel 6 is not available for AVHRR images, we qualitatively assess the virtual channel 6 for several AVHRR images.

Srivastava, Ashok↗

Optimization of an oligonucleotide microchip for microbial identification studies: a non-equilibrium dissociation approach

The utility of a high-density oligonucleotide microarray (microchip) for identifying strains of five closely related bacilli (Bacillus anthracis, Bacillus cereus, Bacillus mycoides, Bacillus medusa and Bacillus subtilis) was demonstrated using an approach that compares the non-equilibrium dissociation rates ('melting curves') of all probe-target duplexes simultaneously. For this study, a hierarchical set of 30 oligonucleotide probes targeting the 16S ribosomal RNA of these bacilli at multiple levels of specificity (approximate taxonomic ranks of domain, kingdom, order, genus and species) was designed and immobilized in a high-density matrix of gel pads on a glass slide. Reproducible melting curves for probes with different levels of specificity were obtained using an optimized salt concentration. Clear discrimination between perfect match (PM) and mismatch (MM) duplexes was achieved. By normalizing the signals to an internal standard (a universal probe), a more than twofold discrimination (> 2.4x) was achieved between PM and 1-MM duplexes at the dissociation temperature at which 50% of the probe-target duplexes remained intact. This provided excellent differentiation among representatives of different Bacillus species, both individually and in mixtures of two or three. The overall pattern of hybridization derived from this hierarchical probe set also provided a clear 'chip fingerprint' for each of these closely related Bacillus species.

Non-NASA Center↗

Dynamics of the spatial scale of visual attention revealed by brain event-related potentials

The temporal dynamics of the spatial scaling of attention during visual search were examined by recording event-related potentials (ERPs). A total of 16 young participants performed a search task in which the search array was preceded by valid cues that varied in size and hence in precision of target localization. The effects of cue size on short-latency (P1 and N1) ERP components, and the time course of these effects with variation in cue-target stimulus onset asynchrony (SOA), were examined. Reaction time (RT) to discriminate a target was prolonged as cue size increased. The amplitudes of the posterior P1 and N1 components of the ERP evoked by the search array were affected in opposite ways by the size of the precue: P1 amplitude increased whereas N1 amplitude decreased as cue size increased, particularly following the shortest SOA. The results show that when top-down information about the region to be searched is less precise (larger cues), RT is slowed and the neural generators of P1 become more active, reflecting the additional computations required in changing the spatial scale of attention to the appropriate element size to facilitate target discrimination. In contrast, the decrease in N1 amplitude with cue size may reflect a broadening of the spatial gradient of attention. The results provide electrophysiological evidence that changes in the spatial scale of attention modulate neural activity in early visual cortical areas and activate at least two temporally overlapping component processes during visual search.

Non-NASA Center↗

Dynamic balance control in elders: gait initiation assessment as a screening tool

OBJECTIVE: To determine whether measurements of center of gravity-center of pressure separation (CG-CP moment arm) during gait initiation can differentiate healthy from disabled subjects with sufficient specificity and sensitivity to be useful as a screening test for dynamic balance in elderly patients. SUBJECTS: Three groups of elderly subjects (age, 74.97+/-6.56 yrs): healthy elders (HE, n = 21), disabled elders (DE, n = 20), and elders with vestibular hypofunction (VH, n = 18). DESIGN: Cross-sectional, intact-groups research design. Peak CG-CP moment arm measures how far the subject will tolerate the whole-body CG to deviate from the ground reaction force's CP; it represents dynamic balance control. Screening test cutoff points at 16 to 18 cm peak CG-CP moment arm predicted group membership. RESULTS: The magnitude of peak CG-CP moment arm was significantly greater in HE than in DE and VH subjects (p<.01) and was not different between the DE and VH groups. The peak CG-CP moment arm occurred at the end of single stance phase in all groups. As a screening test, the peak moment arm has greater than 50% sensitivity and specificity to discriminate the HE group from the DE and VH groups with peak CG-CP moment arm cutoff points between 16 and 18 cm. CONCLUSIONS: Examining dynamic balance through the use of the CG-CP moment arm during single stance in gait initiation discriminates between nondisabled and disabled older persons and warrants further investigation as a potential tool to identify people with balance dysfunction.

NASA Discipline Neuroscience↗

Effect of altered sensory conditions on multivariate descriptors of human postural sway

Multivariate descriptors of sway were used to test whether altered sensory conditions result not only in changes in amount of sway but also in postural coordination. Eigenvalues and directions of eigenvectors of the covariance of shnk and hip angles were used as a set of multivariate descriptors. These quantities were measured in 14 healthy adult subjects performing the Sensory Organization test, which disrupts visual and somatosensory information used for spatial orientation. Multivariate analysis of variance and discriminant analysis showed that resulting sway changes were at least bivariate in character, with visual and somatosensory conditions producing distinct changes in postural coordination. The most significant changes were found when somatosensory information was disrupted by sway-referencing of the support surface (P = 3.2 x 10(-10)). The resulting covariance measurements showed that subjects not only swayed more but also used increased hip motion analogous to the hip strategy. Disruption of vision, by either closing the eyes or sway-referencing the visual surround, also resulted in altered sway (P = 1.7 x 10(-10)), with proportionately more motion of the center of mass than with platform sway-referencing. As shown by discriminant analysis, an optimal univariate measure could explain at most 90% of the behavior due to altered sensory conditions. The remaining 10%, while smaller, are highly significant changes in posture control that depend on sensory conditions. The results imply that normal postural coordination of the trunk and legs requires both somatosensory and visual information and that each sensory modality makes a unique contribution to posture control. Descending postural commands are multivariate in nature, and the motion at each joint is affected uniquely by input from multiple sensors.

NASA Discipline Neuroscience↗

Misperceptions of angular velocities influence the perception of rigidity in the kinetic depth effect

Accuracy in discriminating rigid from nonrigid motion was investigated for orthographic projections of three-dimension rotating objects. In 3 experiments the hypothesis that magnitudes of angular velocity are misperceived in the kinetic depth effect was tested, and in 4 other experiments the hypothesis that misperceiving angular velocities leads to misperceiving rigidity was tested. The principal findings were (a) the magnitude of perceived angular velocity is derived heuristically as a function of a property of the first-order optic flow called deformation and (b) perceptual performance in discriminating rigid from nonrigid motion is accurate in cases when the variability of the deformations of the individual triplets of points of the stimulus displays favors this interpretation and not accurate in other cases.

NASA Center ARC↗

Perceived visual speed constrained by image segmentation

Little is known about how or where the visual system parses the visual scene into objects or surfaces. However, it is generally assumed that the segmentation and grouping of pieces of the image into discrete entities is due to 'later' processing stages, after the 'early' processing of the visual image by local mechanisms selective for attributes such as colour, orientation, depth, and motion. Speed perception is also thought to be mediated by early mechanisms tuned for speed. Here we show that manipulating the way in which an image is parsed changes the way in which local speed information is processed. Manipulations that cause multiple stimuli to appear as parts of a single patch degrade speed discrimination, whereas manipulations that perceptually divide a single large stimulus into parts improve discrimination. These results indicate that processes as early as speed perception may be constrained by the parsing of the visual image into discrete entities.

NASA Discipline Neuroscience↗

Surface Clutter Removal in Airborne Radar Sounding Data from the Dry Valleys, Antarctica

We have collected roughly 1,000 line-km of airborne radar sounding data over glaciers, rock/ice glaciers, permafrost, subsurface ice bodies, ice-covered saline lakes, and glacial deposits in Taylor and Beacon Valley. These data are being analyzed in order to develop techniques for discriminating between subsurface and off-nadir echoes and for detecting and characterizing subsurface interfaces. The identification of features on Mars exhibiting morphologies consistent with ice/rock mixtures, near-surface ice bodies and near-surface liquid water, and the importance of such features to the search for water on Mars, highlights the need for appropriate terrestrial analogs and analysis techniques in order to prepare for radar sounder missions to Mars. Climatic, hydrological, and geological conditions in the Dry Valleys of Antarctica are analogous in many ways to those on Mars. A crucial first step in the data analysis process is the discrimination of echo sources in the radar data. The goal is to identify all returns from the surface of off-nadir topography in order to positively identify subsurface echoes. This process will also be critical for radar data that will be collected in areas of Mars exhibiting significant topography, so that subsurface echoes are identified unambiguously. The positive detection and characterization of subsurface (including sub-ice) water is a primary goal of NASA's Mars exploration program. Our data over the Dry Valleys provides an opportunity to implement techniques we are developing to accomplish these goals.

Holt, J. W.↗

Extracting Olivine (Fo-Fa) Compositions from Raman Spectral Peak Positions

Olivine and pyroxene are two major basaltic minerals that have been identified at Gusev Crater and Meridiani Planum by the Mars Exploration Rovers. Full petrologic characterization of a sample (rock or soil), however, requires determining the range of mineral compositions, extent of zoning, range of grain sizes, mineral associations, presence of xenocrysts, etc. Information of this sort will aid the interpretation of sample crystallization and differentiation histories and help discriminate between lithologies. In Raman spectroscopic experiments, minerals are identified by their spectral patterns and mineral compositions can be inferred from the peak positions. Instruments currently in use or slated for impending surface exploration missions provide only average elemental compositions for relatively large rock or soil targets or bulk mineral analysis. No techniques currently in use or scheduled for flight can characterize both structure and composition of individual mineral grains, in-situ, like the Mars Microbeam Raman Spectrometer (MMRS). The MMRS is designed to take 100 spectra along a 1 cm linear traverse on the surface of a sample, with contributions from one or a few mineral phases per spectrum. We presented a method to extract structural and compositional information from the Raman spectra of quadrilateral pyroxenes. The pyroxene calibration was applied to a Raman spectroscopic study of Martian meteorite EETA79001 along with a preliminary olivine calibration, where we demonstrated the capability to discriminate related lithologies using Raman point counts. This paper presents an improved olivine calibration that will further aid sample characterization and the study of alteration processes.

Kuebler, K.↗

Usefulness of Derived Frank Lead Parameters in Screening for Coronary Artery Disease and Cardiomyopathy

We investigated the accuracy of several known as well as newly-introduced derived Frank-lead ECG parameters in differentiating healthy individuals from patients with obstructive coronary artery disease (CAD) and cardiomyopathy (CM). Advanced high-fidelity 12-lead ECG tests (approx. 5-min supine) were first performed on a "training set" of 99 individuals: 33 with ischemic or dilated CM and low ejection fraction (EF less than 40%); 33 with catheterization-proven obstructive CAD but normal EF; and 33 age-/gender-matched healthy controls. The following derived Frank lead parameters were studied for their accuracy in detecting CAD and CM: the spatial ventricular gradient (VG), including its beat-to-beat coefficient of variability (VG CV); the spatial mean QRS (SM-QRS) and T-waves (SM-T) and their beat-to-beat coefficients of variability; the spatial ventricular activation time (VAT); the mean and maximum spatial QRS-T angles; and standard late potentials parameters (RMS40, fQRSD and LAS). Several of these parameters were accurate in discriminating between the control group and both diseased groups at p less than 0.0001. For example the fQRSD, VG CV, mean spatial QRS-T angle and VG minus SM-QRS (which is similar to the SM-T) had retrospective areas under the ROC curve of 0.78, 0.78, 0.80, and 0.84 (CAD vs. controls) and 0.93, 0.88, 0.98 and 0.99 (CM vs. controls), respectively. The single most effective parameter in discriminating between the CAD and CM groups was the spatial VAT (44 plus or minus 5.8 vs. 53 plus or minus 9.9 ms, p less than 0.0001), with an area under the ROC curve of 0.80. Since subsequent prospective analyses using new groups of patients and healthy subjects have yielded only slightly less accurate results, we conclude that derived Frank-lead parameters show great promise for potentially contributing to the development of a rapid and inexpensive resting ECG-based screening test for heart disease.

DePalma, J. L.↗

Differences in the Optical Characteristics of Continental US Ground and Cloud Flashes as Observed from Space

Continental US lightning flashes observed by the Optical Transient Detector (OTD) are categorized according to flash type (ground or cloud flash) using US National Lightning Detection Network (TM) (NLDN) data. The statistics of the ground and cloud flash optical parameters (e.g., radiance, area, duration, number of optical groups, and number of optical events) are inter-compared. On average, the ground flash cloud-top emissions are more radiant, illuminate a larger area, are longer lasting, and have more optical groups and optical events than those cloud-top emissions associated with cloud flashes. Given these differences, it is suggested that the methods of Bayesian Inference could be used to help discriminate between ground and cloud flashes. The ability to discriminate flash type on-orbit is highly desired since such information would help researchers and operational decision makers better assess the intensification, evolutionary state, and severe weather potential of thunderstorms. This work supports risk reduction activities presently underway for the future launch of the GOES-R Geostationary Lightning Mapper (GLM).

Koshak, William↗

Comparison of the MODIS Multilayer Cloud Detection and Thermodynamic Phase Products with CALIPSO and CloudSat

CALIPSO and CloudSat, launched in June 2006, provide global active remote sensing measurements of clouds and aerosols that can be used for validation of a variety of passive imager retrievals derived from instruments flying on the Aqua spacecraft and other A-Train platforms. The most recent processing effort for the MODIS Atmosphere Team, referred to as the "Collection 5" stream, includes a research-level multilayer cloud detection algorithm that uses both thermodynamic phase information derived from a combination of solar and thermal emission bands to discriminate layers of different phases, as well as true layer separation discrimination using a moderately absorbing water vapor band. The multilayer detection algorithm is designed to provide a means of assessing the applicability of 1D cloud models used in the MODIS cloud optical and microphysical product retrieval, which are generated at a 1 h resolution. Using pixel-level collocations of MODIS Aqua, CALIOP, and CloudSat radar measurements, we investigate the global performance of the thermodynamic phase and multilayer cloud detection algorithms.

Platnick, Steven↗

Electron Calorimeter Experiment

Boron loaded scintillators are suitable for measuring secondary neutrons produced by high-energy particles: protons & electrons Neutron flux can be used to discriminate hadron and electro-magnetic particles Combined effectiveness of all e/p discriminators techniques employedTBD Only moderate improvement in detection efficiency for B-10 concentrations >few% in thick moderators Bottom scintillator might serve as cascade penetration counter (TBC)

Adams, James H.↗

Software Simulates Sight: Flat Panel Mura Detection

In the increasingly sophisticated world of high-definition flat screen monitors and television screens, image clarity and the elimination of distortion are paramount concerns. As the devices that reproduce images become more and more sophisticated, so do the technologies that verify their accuracy. By simulating the manner in which a human eye perceives and interprets a visual stimulus, NASA scientists have found ways to automatically and accurately test new monitors and displays. The Spatial Standard Observer (SSO) software metric, developed by Dr. Andrew B. Watson at Ames Research Center, measures visibility and defects in screens, displays, and interfaces. In the design of such a software tool, a central challenge is determining which aspects of visual function to include while accuracy and generality are important, relative simplicity of the software module is also a key virtue. Based on data collected in ModelFest, a large cooperative multi-lab project hosted by the Optical Society of America, the SSO simulates a simplified model of human spatial vision, operating on a pair of images that are viewed at a specific viewing distance with pixels having a known relation to luminance. The SSO measures the visibility of foveal spatial patterns, or the discriminability of two patterns, by incorporating only a few essential components of vision. These components include local contrast transformation, a contrast sensitivity function, local masking, and local pooling. By this construction, the SSO provides output in units of "just noticeable differences" (JND) a unit of measure based on the assumed smallest difference of sensory input detectable by a human being. Herein is the truly amazing ability of the SSO, while conventional methods can manipulate images, the SSO models human perception. This set of equations actually defines a mathematical way of working with an image that accurately reflects the way in which the human eye and mind behold a stimulus. The SSO is intended for a wide variety of applications, such as evaluating vision from unmanned aerial vehicles, measuring visibility of damage to aircraft and to the space shuttles, predicting outcomes of corrective laser eye surgery, inspecting displays during the manufacturing process, estimating the quality of compressed digital video, evaluating legibility of text, and predicting discriminability of icons or symbols in a graphical user interface.

Source record↗

Hail Monitor Sensor

An inexpensive and simple hail monitor design has been developed that has a single piezoelectric ceramic disc and uses a metal plate as a sounding board. The structure is durable and able to withstand the launch environment. This design has several advantages over a multi-ceramic sensor, including reduced cost and complexity, increased durability, and improvement in impact response uniformity over the active surface. However, the most important characteristic of this design is the potential to use frequency discrimination between the spectrum created from raindrop impact and a hailstone impact. The sound of hail hitting a metal plate is distinctly different from the sound of rain hitting the same plate. This fortuitous behavior of the pyramid sensor may lead to a signal processing strategy, which is inherently more reliable than one depending on amplitude processing only. The initial concept has been im proved by forming a shallow pyramid structure so that hail is encouraged to bounce away from the sensor so as not to be counted more than once. The sloped surface also discourages water from collecting. Additionally, the final prototype version includes a mounting box for the piezo-ceramic, which is offset from the pyramid apex, thus helping to reduce non-uniform response (see Figure 2). The frequency spectra from a single raindrop impact and a single ice ball impact have been compared. The most notable feature of the frequency resonant peaks is the ratio of the 5.2 kHz to 3.1 kHz components. In the case of a raindrop, this ratio is very small. But in the case of an ice ball, the ratio is roughly one third. This frequency signature of ice balls should provide a robust method for discriminating raindrops from hailstones. Considering that hail size distributions (HSDs) and fall rates are roughly 1 percent that of rainfall, hailstone sizes range from a few tenths of a centimeter to several centimeters. There may be considerable size overlap between large rain and small hail. As hail occurs infrequently at KSC, the ideal HSD measurement sensor needs to have a collection area roughly 100 times greater than a raindrop-size distribution sensor or disdrometer. The sensitivity should be such that it can detect and count very small hail in the midst of intense rainfall consisting of large raindrop sizes. The dynamic range and durability should allow measurement of the largest hail sizes, and the operation and calibration strategy should consider the infrequent occurrence of hail fall over the KSC area.

Younquist, Robert↗