Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Sensitivity profiles”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,063 records · Page 59

Airborne Lidar Measurements of Atmospheric Pressure Made Using the Oxygen A-Band

Accurate measurements of greenhouse gas mixing ratios on a global scale are currently needed to gain a better understanding of climate change and its possible impact on our planet. In order to remotely measure greenhouse gas concentrations in the atmosphere with regard to dry air, the air number density in the atmosphere is also needed in deriving the greenhouse gas concentrations. Since oxygen is stable and uniformly mixed in the atmosphere at 20.95%, the measurement of an oxygen absorption in the atmosphere can be used to infer the dry air density and used to calculate the dry air mixing ratio of a greenhouse gas, such as carbon dioxide or methane. OUT technique of measuring Oxygen uses integrated path differential absorption (IPDA) with an Erbium Doped Fiber Amplifier (EDF A) laser system and single photon counting module (SPCM). It measures the absorbance of several on- and off-line wavelengths tuned to an O2 absorption line in the A-band at 764.7 nm. The choice of wavelengths allows us to maximize the pressure sensitivity using the trough between two absorptions in the Oxygen A-band. Our retrieval algorithm uses ancillary meteorological and aircraft altitude information to fit the experimentally obtained lidar O2 line shapes to a model atmosphere and derives the pressure from the profiles of the two lines. We have demonstrated O2 measurements from the ground and from an airborne platform. In this paper we will report on our airborne measurements during our 2011 campaign for the ASCENDS program.

Riris, Haris↗

An Overview of the TROPICS NASA Earth Venture Mission

The Time-Resolved Observations of Precipitation structure and storm Intensity with a Constellation of Smallsats (TROPICS) mission was selected by NASA as part of the Earth Venture-Instrument (EVI-3) program. The overarching goal for TROPICS is to provide nearly all-weather observations of 3D temperature and humidity, as well as cloud ice and precipitation horizontal structure, at high temporal resolution to conduct high-value science investigations of tropical cyclones. TROPICS will provide rapid-refresh microwave measurements (median refresh rate better than 60 min for the baseline mission) which can be used to observe the thermodynamics of the troposphere and precipitation structure for storm systems at the mesoscale and synoptic scale over the entire storm life cycle. TROPICS comprises six Cube-Sats in three low-Earth orbital planes. Each CubeSat will host a high-performance radiometer to provide temperature profiles using seven channels near the 118.75 GHz oxygen absorption line, water vapour profiles using three channels near the 183 GHz water vapour absorption line, imagery in a single channel near 90 GHz for precipitation measurements (when combined with higher-resolution water vapour channels), and a single channel near 205 GHz which is more sensitive to precipitation-sized ice particles. This observing system offers an unprecedented combination of horizontal and temporal resolution to measure environmental and inner-core conditions for tropical cyclones on a nearly global scale and is a major leap forward in the temporal resolution of several key parameters needed for assimilation into advanced data assimilation systems capable of utilizing rapid-update radiance or retrieval data.Launch readiness is currently projected for late 2019.

TROPICS↗

Using Importance Sampling Monte Carlo to Analyze Aircraft Takeoff and Landing

Aircraft have achieved high levels of reliability, so the probability of undesirable dynamics is very low. The low probability of a bad takeoff or landing challenges nondeterministic methods to quantify the uncertainty of these improbable events. In the present work, a Monte Carlo method is defined to more effectively quantify these unlikely events that is suitable for uncertainty analysis of a mature design with many uncertainty parameters. The proposed Monte Carlo method has been applied to the takeoff and landing of the X-59 Quiet SuperSonic Technology (QueSST). Takeoff and landing simulation profiles were defined using a combination of industry standards and piloted simulation experience. The proposed method is shown to be able to quantify events with significantly fewer samples than would be required with conventional Monte Carlo. These results improve understanding of the sensitivity of the takeoff and landing dynamics to inform further studies and test planning.

Jeffrey Ouellette↗

Using Importance Sampling Monte Carlo to Analyze Aircraft Takeoff and Landing

Aircraft have achieved high levels of reliability, so the probability of undesirable dynamics is very low. The low probability of a bad takeoff or landing challenges nondeterministic methods to quantify the uncertainty of these improbable events. In the present work, a Monte Carlo method is defined to more effectively quantify these unlikely events that is suitable for uncertainty analysis of a mature design with many uncertainty parameters. The proposed Monte Carlo method has been applied to the takeoff and landing of the X-59 Quiet SuperSonic Technology (QueSST). Takeoff and landing simulation profiles were defined using a combination of industry standards and piloted simulation experience. The proposed method is shown to be able to quantify events with significantly fewer samples than would be required with conventional Monte Carlo. These results improve understanding of the sensitivity of the takeoff and landing dynamics to inform further studies and test planning.

Jeffrey Ouellette↗

Requirements for an Advanced Low Earth Orbit (LEO) Sounder (ALS) for Improved Regional Weather Prediction and Monitoring of Greenhouse Gases

Hyperspectral infrared atmospheric sounders (e.g., the Atmospheric Infrared Sounder (AIRS) on Aqua and the Infrared Atmospheric Sounding Interferometer (IASI) on Met Op) provide highly accurate temperature and water vapor profiles in the lower to upper troposphere. These systems are vital operational components of our National Weather Prediction system and the AIRS has demonstrated over 6 hrs of forecast improvement on the 5 day operational forecast. Despite the success in the mid troposphere to lower stratosphere, a reduction in sensitivity and accuracy has been seen in these systems in the boundary layer over land. In this paper we demonstrate the potential improvement associated with higher spatial resolution (1 km vs currently 13.5 km) on the accuracy of boundary layer products with an added consequence of higher yield of cloud free scenes. This latter feature is related to the number of samples that can be assimilated and has also shown to have a significant impact on improving forecast accuracy. We also present a set of frequencies and resolutions that will improve vertical resolution of temperature and water vapor and trace gas species throughout the atmosphere. Development of an Advanced Low Earth Orbit (LEO) Sounder (ALS) with these improvements will improve weather forecast at the regional scale and of tropical storms and hurricanes. Improvements are also expected in the accuracy of the water vapor and cloud properties products, enhancing process studies and providing a better match to the resolution of future climate models. The improvements of technology required for the ALS are consistent with the current state of technology as demonstrated in NASA Instrument Incubator Program and NOAA's Hyperspectral Environmental Suite (HES) formulation phase development programs.

temperature↗

Inclusion of Linearized Moist Physics in Nasa's Goddard Earth Observing System Data Assimilation Tools

Inclusion of moist physics in the linearized version of a weather forecast model is beneficial in terms of variational data assimilation. Further, it improves the capability of important tools, such as adjoint-based observation impacts and sensitivity studies. A linearized version of the relaxed Arakawa-Schubert (RAS) convection scheme has been developed and tested in NASA's Goddard Earth Observing System data assimilation tools. A previous study of the RAS scheme showed it to exhibit reasonable linearity and stability. This motivates the development of a linearization of a near-exact version of the RAS scheme. Linearized large-scale condensation is included through simple conversion of supersaturation into precipitation. The linearization of moist physics is validated against the full nonlinear model for 6- and 24-h intervals, relevant to variational data assimilation and observation impacts, respectively. For a small number of profiles, sudden large growth in the perturbation trajectory is encountered. Efficient filtering of these profiles is achieved by diagnosis of steep gradients in a reduced version of the operator of the tangent linear model. With filtering turned on, the inclusion of linearized moist physics increases the correlation between the nonlinear perturbation trajectory and the linear approximation of the perturbation trajectory. A month-long observation impact experiment is performed and the effect of including moist physics on the impacts is discussed. Impacts from moist-sensitive instruments and channels are increased. The effect of including moist physics is examined for adjoint sensitivity studies. A case study examining an intensifying Northern Hemisphere Atlantic storm is presented. The results show a significant sensitivity with respect to moisture.

Convection↗

Descriptive and sensitivity analyses of WATBALI: A dynamic soil water model

A soil water computer model that uses the IBM Continuous System Modeling Program III to solve the dynamic equations representing the soil, plant, and atmospheric physical or physiological processes considered is presented and discussed. Using values describing the soil-plant-atmosphere characteristics, the model predicts evaporation, transpiration, drainage, and soil water profile changes from an initial soil water profile and daily meteorological data. The model characteristics and simulations that were performed to determine the nature of the response to controlled variations in the input are described the results of the simulations are included and a change that makes the response of the model more closely represent the observed characteristics of evapotranspiration and profile changes for dry soil conditions is examined.

Hildreth, W. W.↗

Laboratory and On-Sky Validation of the Shaped Pupil Coronagraph's Sensitivity to Low-Order Aberrations with Active Wavefront Control

We present early laboratory simulations and extensive on-sky tests validating of the performance of a shaped pupil coronagraph (SPC) behind an extreme-AO (Adaptive Optics) corrected beam of the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system. In tests with the SCExAO internal source/wavefront error simulator, the normalized intensity profile for the SPC degrades more slowly than for the Lyot coronagraph as low-order aberrations reduce the Strehl ratio (S.R.) from extremely high values (S.R. approximately 0.93-0.99) to those characteristic of current ground-based extreme AO systems (S.R. approximately 0.74-0.93) and then slightly lower values down to S.R. approximately 0.57. On-sky SCExAO data taken with the SPC and other coronagraphs for brown dwarf/planet-hosting stars HD 1160 and HR 8799 provide further evidence for the SPC's robustness to low-order aberrations. From H-band Strehl ratios of 80 percent to 70 percent, the Lyot coronagraph's performance versus that of the SPC may degrade even faster on sky than is seen in our internal source simulations. The 5-sigma contrast also degrades faster (by a factor of two) for the Lyot than the SPC. The SPC we use was designed as a technology demonstrator only, with a contrast floor, throughput, and outer working angle poorly matched for SCExAO's current AO performance and poorly tuned for imaging the HR 8799 planets. Nevertheless, we detect HR 8799 cde with SCExAO/CHARIS using the SPC in broadband mode, where the signal-to-noise ratio for planet e is within 30 percent of that obtained using the vortex coronagraph. The shaped-pupil coronagraph is a promising design demonstrated to be robust in the presence of low-order aberrations and may be well-suited for future ground and space-based direct imaging observations, especially those focused on follow-up exoplanet characterization and technology demonstration of deep contrast within well-defined regions of the image plane.

Currie, Thayne↗

Tracing cosmic gas in filaments and halos: Low-redshift insights from the kinematic Sunyaev-Zel’dovich effect

In this work, we leverage cosmic microwave background (CMB) data from the Atacama Cosmology Telescope (ACT) and LSS data from the imaging survey conducted by the Dark Energy Spectroscopic Instrument (DESI) to study the distribution of gas around galaxy groups at low redshift, z ≈ 0.3, via the kinematic Sunyaev-Zel'dovich (kSZ) effect. In particular, we perform velocity-weighted stacking on the photometric galaxies from the Bright Galaxy Survey (BGS) to isolate the monopole and quadrupole of the kSZ signal, orienting the stacked images along 2D filaments identified using the Hessian of the projected gravitational potential. We find a 7.2σ detection in the monopole of the signal (i.e., the gas density profile) and a 4σ detection in the quadrupole (m = 2), constituting the first measurement of the alignment between gas distribution and the cosmic web through the kSZ effect. As it is a linear probe of the local gas density, the kSZ has heightened sensitivity to the warm-hot intergalactic medium (WHIM), which is believed to house the majority of the "missing baryons."Mapping out the gas density at low redshifts, as enabled by our measurements, is crucial for weak lensing surveys, for which the impact of baryons on small scales is a major impediment. We compare the anisotropic signal against two hydrodynamical simulations, TNG300-1 and Illustris, which have very different baryonic feedback prescriptions. We find that the anisotropic signal measured in the data is comparable but slightly larger and more extended compared with the simulations. Further, this suggests that there is excess accretion and feedback taking place through the filaments, hinting at the possible presence of spin-filament alignment of the BGS objects.

79 ASTRONOMY AND ASTROPHYSICS↗

Quantum Enhanced Tracker (Final Report)

A new concept of charged particle detector, called Quantum Enhanced Tracker (QET) is proposed and intended for optical imaging of charged particle tracks. We present a quantum-based detection method for reconstructing the spatial profile of an electron beam by passing it through a dilute vapor of rubidium atoms. The perturbation of the atomic spin’s quantum state by the electron beam’s magnetic field is detected via nonlinear magneto-optical polarization rotation. Consequently, the electron beam’s position, size and current density can be measured, and its transverse profile reconstructed by analyzing the polarization rotation of a transverse probe laser. This method was experimentally studied using e-beams with currents ranging from 1 to 200 μA and energies between 10 to 20 keV. The results show that this approach is sensitive to the e-beam current and independent of e-beam energy. This technique provides a potentially 3-D capable approach for non-invasive characterization and monitoring of charged particles used in accelerators and nuclear physics research.

43 PARTICLE ACCELERATORS↗

Dual-frequency (Ka-band and G-band) radar estimates of liquid water content profiles in shallow clouds

The profile of the liquid water content (LWC) in clouds provides fundamental information for understanding the internal structure of clouds, their radiative effects, propensity to precipitate, and degree of entrainment and mixing with the surrounding environment. In principle, differential absorption techniques based on coincident dual-frequency radar reflectivity observations have the potential to provide the LWC profile. Previous differential frequency radar reflectivity (DFR) efforts were challenged by the fact that the measurable differential attenuation for small quantities of LWC is usually comparable to the system measurement error. This typically renders the retrieval impractical, as the uncertainty can become many times greater than the retrieved value itself. Theoretically, this drawback can be mitigated following two interconnected approaches: (1) increasing the frequency separation between the dual-frequency radar system to measure greater differential attenuation and (2) increasing the radar operating frequency to reduce the instrument measurement random error. Our recently developed 239 GHz radar was deployed during the Eastern Pacific Cloud Aerosol Precipitation Experiment (EPCAPE) along with a variety of collocated remote sensing and in situ instruments. We have combined Ka-band (35 GHz) and G-band (239 GHz) observations to retrieve the LWC from more than 100 vertical profiles of shallow clouds with typical amounts of LWC smaller than 1 g m -3 . We theoretically and experimentally demonstrate that the Ka-band and G-band pair of frequencies offers at least a 65 % relative improvement in the LWC retrieval sensitivity compared to previous works reported in the literature using lower-frequency radars. This new technique provides a missing capability to determine the LWC in the challenging low liquid water path (LWP) range (< 200 g m -2 ) and suggests a way forward to characterize microphysical and dynamical processes more precisely in shallow clouds.

54 ENVIRONMENTAL SCIENCES↗

Remote sensing of the ozone profile in the lower stratosphere using UV and IR measurements from Nimbus 4

With a three-parameter analytical model, the ozone profile below 10 mbar to the surface is derived from the Nimbus 4 satellite backscattered ultraviolet and infrared measurements. Comparison of the derived profiles with those observed by ozonesondes shows that gross features are satisfactorily reproduced. Meridional cross section of the ozone partial pressure derived from the satellite data reveal the significant equator-to-pole features, as well as seasonal variability. An examination of the sensitivity of the method shows that an error in infrared radiance of approximately 1 erg leads to an error of about 10 mbar in the weighted mean pressure of the ozone layer in the tropics.

Prabhakara, C.↗

Smoke and dust particles of meteoric origin in the mesosphere and stratosphere

A height profile of ablated mass from meteors is calculated, assuming an incoming mass of 10 to the -16th g/sq cm/s (44 metric tons per day) and the velocity distribution of Southworth and Sekanina, which has a mean of 14.5 km/s. The profile peaks at 84 km. The fluxes of micrometeorites and residual meteoroids are also calculated. The coagulation of the evaporated silicates into 'smoke' particles is then followed by means of a model adapted from a previous study of the stratospheric sulfate layer. Numerous sensitivity tests are made. Features of the results are a sharp cutoff of the particle distribution above 90 km, and a surface area close to 10 to the -9th sq cm/cu cm all the way from 30 to 85 km. Some confirmation is obtained from balloon studies of condensation nuclei, although the various measurements differ greatly. The optical scattering and extinction are shown to be undetectable. Several potential applications are suggested: nucleation of sulfate particles and noctilucent clouds, scavenging of metallic ions and atoms, and perhaps other aeronomical effects. The latter are limited to processes that can be influenced by a collision time of the order of a day.

Hunten, D. M.↗

Retrieving the Vertical Structure of the Effective Aerosol Complex Index of Refraction from a Combination of Aerosol in Situ and Remote Sensing Measurements During TARFOX

The largest uncertainty in estimates of the effects of atmospheric aerosols on climate stems from uncertainties in the determination of their microphysical properties, including the aerosol complex index of refraction, which in turn determines their optical properties. A novel technique is used to estimate the aerosol complex index of refraction in distinct vertical layers from a combination of aerosol in situ size distribution and remote sensing measurements during the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX). In particular, aerosol backscatter measurements using the NASA Langley LASE (Lidar Atmospheric Sensing Experiment) instrument and in situ aerosol size distribution data are utilized to derive vertical profiles of the "effective" aerosol complex index of refraction at 815 nm (i.e., the refractive index that would provide the same backscatter signal in a forward calculation on the basis of the measured in situ particle size distributions for homogeneous, spherical aerosols). A sensitivity study shows that this method yields small errors in the retrieved aerosol refractive indices, provided the errors in the lidar-derived aerosol backscatter are less than 30% and random in nature. Absolute errors in the estimated aerosol refractive indices are generally less than 0.04 for the real part and can be as much as 0.042 for the imaginary part in the case of a 30% error in the lidar-derived aerosol backscatter. The measurements of aerosol optical depth from the NASA Ames Airborne Tracking Sunphotometer (AATS-6) are successfully incorporated into the new technique and help constrain the retrieved aerosol refractive indices. An application of the technique to two TARFOX case studies yields the occurrence of vertical layers of distinct aerosol refractive indices. Values of the estimated complex aerosol refractive index range from 1.33 to 1.45 for the real part and 0.001 to 0.008 for the imaginary part. The methodology devised in this study provides, for the first time, a complete set of vertically resolved aerosol size distribution and refractive index data. yielding the vertical distribution of aerosol optical properties required for the determination of aerosol-induced radiative flux changes.

Redemann, J.↗

Retrieving the Vertical Structure of the Effective Aerosol Complex Index of Refraction from a Combination of Aerosol in Situ and Remote Sensing Measurements During TARFOX

The largest uncertainty in estimates of the effects of atmospheric aerosols on climate stems from uncertainties in the determination of their microphysical properties, including the aerosol complex index of refraction, which in turn determines their optical properties. A novel technique is used to estimate the aerosol complex index of refraction in distinct vertical layers from a combination of aerosol in situ size distribution and remote sensing measurements during the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX). In particular, aerosol backscatter measurements using the NASA Langley LASE (Lidar Atmospheric Sensing Experiment) instrument and in situ aerosol size distribution data are utilized to derive vertical profiles of the 'effective' aerosol complex index of refraction at 815 nm (i.e., the refractive index that would provide the same backscatter signal in a forward calculation on the basis of the measured in situ particle size distributions for homogeneous, spherical aerosols). A sensitivity study shows that this method yields small errors in the retrieved aerosol refractive indices, provided the errors in the lidar derived aerosol backscatter are less than 30% and random in nature. Absolute errors in the estimated aerosol refractive indices are generally less than 0.04 for the real part and can be as much as 0.042 for the imaginary part in the case of a 30% error in the lidar-derived aerosol backscatter. The measurements of aerosol optical depth from the NASA Ames Airborne Tracking Sunphotometer (AATS-6) are successfully incorporated into the new technique and help constrain the retrieved aerosol refractive indices. An application of the technique to two TARFOX case studies yields the occurrence of vertical layers of distinct aerosol refractive indices. Values of the estimated complex aerosol refractive index range from 1.33 to 1.45 for the real part and 0.001 to 0.008 for the imaginary part. The methodology devised in this study provides, for the first time a complete set of vertically resolved aerosol size distribution and refractive index data, yielding the vertical distribution of aerosol optical properties required for the determination of aersol-induced radiative flux changes

Redemann, J.↗

A Generalised Porosity Formalism for Isotropic and Anisotropic Effective Opacity and its Effects on X-ray Line Attenuation in Clumped O Star Winds

We present a generalised formalism for treating the porosity-associated reduction in continuum opacity that occurs when individual clumps in a stochastic medium become optically thick. As in previous work, we concentrate on developing bridging laws between the limits of optically thin and thick clumps. We consider geometries resulting in either isotropic or anisotropic effective opacity, and, in addition to an idealised model in which all clumps have the same local overdensity and scale, we also treat an ensemble of clumps with optical depths set by Markovian statistics. This formalism is then applied to the specific case of bound-free absorption of X- rays in hot star winds, a process not directly affected by clumping in the optically thin limit. We find that the Markov model gives surprisingly similar results to those found previously for the single clump model, suggesting that porous opacity is not very sensitive to details of the assumed clump distribution function. Further, an anisotropic effective opacity favours escape of X-rays emitted in the tangential direction (the venetian blind effect), resulting in a bump of higher flux close to line centre as compared to profiles computed from isotropic porosity models. We demonstrate how this characteristic line shape may be used to diagnose the clump geometry, and we confirm previous results that for optically thick clumping to significantly influence X-ray line profiles, very large porosity lengths, defined as the mean free path between clumps, are required. Moreover, we present the first X-ray line profiles computed directly from line-driven instability simulations using a 3-D patch method, and find that porosity effects from such models also are very small. This further supports the view that porosity has, at most, a marginal effect on X-ray line diagnostics in O stars, and therefore that these diagnostics do indeed provide a good clumping insensitive method for deriving O star mass-loss rates.

Sundqvist, Jon O.↗

A Generalised Porosity Formalism for Isotropic and Anisotropic Effective Opacity and Its Effects on X-ray Line Attenuation in Clumped O Star Winds

We present a generalised formalism for treating the porosity-associated reduction in continuum opacity that occurs when individual clumps in a stochastic medium become optically thick. As in previous work, we concentrate on developing bridging laws between the limits of optically thin and thick clumps. We consider geometries resulting in either isotropic or anisotropic effective opacity, and, in addition to an idealised model in which all clumps have the same local overdensity and scale, we also treat an ensemble of clumps with optical depths set by Markovian statistics. This formalism is then applied to the specific case of bound-free absorption of X- rays in hot star winds, a process not directly affected by clumping in the optically thin limit. We find that the Markov model gives surprisingly similar results to those found previously for the single clump model, suggesting that porous opacity is not very sensitive to details of the assumed clump distribution function. Further, an anisotropic effective opacity favours escape of X-rays emitted in the tangential direction (the venetian blind effect), resulting in a bump of higher flux close to line centre as compared to profiles computed from isotropic porosity models. We demonstrate how this characteristic line shape may be used to diagnose the clump geometry, and we confirm previous results that for optically thick clumping to significantly influence X-ray line profiles, very large porosity lengths, defined as the mean free path between clumps, are required. Moreover, we present the first X-ray line profiles computed directly from line-driven instability simulations using a 3-D patch method, and find that porosity effects from such models also are very small. This further supports the view that porosity has, at most, a marginal effect on X-ray line diagnostics in O stars, and therefore that these diagnostics do indeed provide a good clumping insensitive method for deriving O star mass-loss rates.

generalised↗

Results of the NASA Kennedy Space Center 50-MHz Doppler Radar Wind Profiler Operational Acceptance Test

This paper presents results of the new Kennedy Space Center (KSC) 50-MHz Doppler Radar Wind Profiler (DRWP) Operational Acceptance Test (OAT). The goal of the OAT was to verify the data quality of the new DRWP against the performance of the previous DRWP in order to use wind data derived by the new DRWP for space launch vehicle operations support at the Eastern Range. The previous DRWP was used as a situational awareness asset for mission operations to identify rapid changes in the wind environment that weather balloons cannot depict. The Marshall Space Flight Center's Natural Environments Branch assessed data from the new DRWP collected during Jan-Feb 2015 against a specified set of test criteria. Data examination verified that the DRWP provides complete profiles every five minutes from 1.8-19.5 km in vertical increments of 150 m. Analysis of 49 concurrent DRWP and balloon profiles presented root mean square wind component differences around 2.0 m/s. Evaluation of the DRWP's coherence between five-minute wind pairs found the effective vertical resolution to be Nyquist-limited at 300 m for both wind components. In addition, the sensitivity to rejecting data that do not have adequate signal was quantified. This paper documents the data, quality control procedures, methodology, and results of each analysis.

Barbre', Robert E., Jr.↗