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NASA NTRS2024

Revised estimates of NO 2 reductions during the COVID-19 lockdowns using updated TROPOMI NO 2 retrievals and model simulations

The TROPOspheric Monitoring Instrument (TROPOMI) observed unprecedented declines in NO 2 vertical column densities (VCD) over the world's most densely populated cities during the 2020 COVID-19 lockdowns. These favorable changes in NO 2 air quality were correlated with sharp reductions in traffic volume and economic activity during the lockdowns. In this comprehensive global study, we provide revised estimates of the declines in anthropogenic emissions for 36 megacities using a novel methodology for disentangling the anthropogenic emissions from the meteorological transport and natural variability. We further quantify the uncertainty associated with changes in the a priori profile shape information during the lockdowns due to reduced emissions. Satellite NO 2 retrieval techniques calculate an air mass factor that requires a priori NO 2 profile shape information representative of the local atmosphere. This information, which is typically obtained from a chemical transport model (CTM), was not available for the early studies. This study also accounts for the satellite sampling errors resulting from the selective sampling of non-cloudy scenes during the study period. For our analysis, we used CTM simulations that were generated with and without COVID-impacted emissions. We perform retrievals of tropospheric NO 2 columns with the NASA NO 2 algorithm, and then use observed and simulated data to disentangle the meteorological transport from the contribution due anthropogenic emissions. We found that the meteorological transport was most significant source of variability ranging between −35% and 22% of the change total tropospheric VCD. We also find that not accounting for changes in the a priori NO 2 profile shape information during the lockdowns resulted in systematic retrieval errors that were up to 12% of the estimated decline, and the elimination of cloud contaminated scenes resulted in sampling errors that in general ranged between varied ±15%.

NO2↗

NASA NTRS2000

On the Spatial Distribution of High Velocity Al-26 Near the Galactic Center

We present results of simulations of the distribution of 1809 keV radiation from the decay of Al-26 in the Galaxy. Recent observations of this emission line using the Gamma Ray Imaging Spectrometer (GRIS) have indicated that the bulk of the AL-26 must have a velocity of approx. 500 km/ s. We have previously shown that a velocity this large could be maintained over the 10(exp 6) year lifetime of the Al-26 if it is trapped in dust grains that are reaccelerated periodically in the ISM. Here we investigate whether a dust grain velocity of approx. 500 km/ s will produce a distribution of 1809 keV emission in latitude that is consistent with the narrow distribution seen by COMPTEL. We find that dust grain velocities in the range 275 - 1000 km/ s are able to reproduce the COMPTEL 1809 keV emission maps reconstructed using the Richardson-Lucy and Maximum Entropy image reconstruction methods while the emission map reconstructed using the Multiresolution Regularized Expectation Maximization algorithm is not well fit by any of our models. The Al-26 production rate that is needed to reproduce the observed 1809 keV intensity yields in a Galactic mass of Al-26 of approx. 1.5 - 2 solar mass which is in good agreement with both other observations and theoretical production rates.

Sturner, Steven J.↗

NASA NTRS1978

Radiative transfer calculated from a Markov chain formalism

The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

Esposito, L. W.↗

NASA NTRS1999

Clustering of the Diffuse Infrared Light from the COBE DIRBE Maps: Power Spectrum Analysis and Excess Isotropic Component of Fluctuations - 3

The cosmic infrared background (CIB) radiation is the cosmic repository for energy release throughout the history of the universe. The spatial fluctuations of the CIB resulting from galaxy clustering are expected to be at least a few percent on scales of a degree, depending on the luminosity and clustering history of the early universe. Using the all-sky data from the COBE DIRBE instrument at wavelengths 1.25 - 100 microns we attempt to measure the CIB fluctuations. In the near-IR, foreground emission is dominated by small scale structure due to stars in the Galaxy. There we find a strong correlation between the amplitude of the fluctuations and Galactic latitude after removing bright foreground stars. Using data outside the Galactic plane (absolute value of b > 20 deg) and away from the center (90 deg < l < 270 deg) we extrapolate the amplitude of the fluctuations to cosec absolute value of b = 0. We find a positive intercept of delta.F(sub rms) = 15.5(sup +3.7, sub -7.0), 5.9(sup +1.6, sub -3.7), 2.4(sup +0.5, sub -0.9), 2.0(sup +0.25, sub -0.5) nW/sq m.sr at 1.25, 2.2, 3.5 and 4.9 microns respectively, where the errors are the range of 92% confidence limits. For color subtracted maps between band 1 and 2 we find the isotropic part of the fluctuations at 7.6(sup +1.2, sub -2.4) nW/sq m.sr. Based on detailed numerical and analytic models, this residual is not likely to originate from the Galaxy, our clipping algorithm, or instrumental noise. We demonstrate that the residuals from the fit used in the extrapolation are distributed isotropically and suggest that this extra variance may result from structure in the CIB. We also obtain a positive intercept from a linear combination of maps at 1.25 and 2.2 microns. For 2 deg < theta < 15 deg, a power-spectrum analysis yields limits of (theta/5 deg) x delta.F(sub rms)(theta) < 6, 2.5, 0.8, 0.5 nW/sq m.sr at 1.25, 2.2, 3.5 and 4.9 microns respectively. From 10 - 100 microns, the dominant foregrounds are emission by dust in the Solar system and the Galaxy. There the upper limits on the CIB fluctuations are below 1 nW/sq m.sr and are lowest (< equal 0.5 nW/sq m.sr) at 25 microns.

Kashlinsky, A.↗

NASA NTRS2009

Autonomously Calibrating a Quadrupole Mass Spectrometer

A computer program autonomously manages the calibration of a quadrupole ion mass spectrometer intended for use in monitoring concentrations and changes in concentrations of organic chemicals in the cabin air of the International Space Station. The instrument parameters calibrated include the voltage on a channel electron multiplier, a discriminator threshold, and an ionizer current. Calibration is achieved by analyzing the mass spectrum obtained while sweeping the parameter ranges in a heuristic procedure, developed by mass spectrometer experts, that involves detection of changes in signal trends that humans can easily recognize but cannot necessarily be straightforwardly codified in an algorithm. The procedure includes calculation of signal-to-noise ratios, signal-increase rates, and background-noise-increase rates; finding signal peaks; and identifying peak patterns. The software provides for several recovery-from-error scenarios and error-handling schemes. The software detects trace amounts of contaminant gases in the mass spectrometer and notifies associated command- and-data-handling software to schedule a cleaning. Furthermore, the software autonomously analyzes the mass spectrum to determine whether the parameters of a radio-frequency ramp waveform are set properly so that the peaks of the mass spectrum are at expected locations.

Lee, Seungwon↗

NASA NTRS2003

Preservation and Enhancement of the Spacewatch Data Archives

In March of 1998, the asteroid 1997 XF11 was announced to be potentially hazardous after being tracked over 90 days. A potential two year wait for confirming observations was shortened to under 24 hours because of the existence of archived photographic prediscovery images. Spacewatch was a pioneer in using CCD scanning and possesses a valuable digital archive of its scans. Unfortunately these data are aging on magnetic tape and will soon be lost. Since 1990, the Spacewatch project gathered some 1.5 Terabytes of scan data covering roughly 75,000 degrees of sky to a limiting magnitude of V = 21.5. The data have not yet been mined for all of their asteroids for scientific studies and orbit determination. Spacewatch's real-time motion detection program MODP was constrained by the computers of the era to use simplified image processing algorithms at a reduced efficiency. Jedicke and Herron estimated MODP's efficiency at finding asteroids to be approximately 60 percent to V=18 and improving somewhat thereafter. This lead to a substantial bias correction in their analyses. Larsen has developed a MODP replacement capable in excess of 90 percent efficiency in the same range and able to push a magnitude fainter in completeness. We propose a program of post-processing and re-archiving Spacewatch data. Our scans would be transferred from tape to CD-ROMs and converted to FITS images -- establishing a consistent data format and media for both past and future Spacewatch observations. Larsen's MODP replacement would mine these data for previously undetected motions, which would be made available to the Minor Planet Center and our ongoing asteroid population studies. A searchable observation record would be made generally available for prediscovery work. We estimate the net asteroid yield of this proposal is equivalent to three full years of Spacewatch operations.

Larsen, Jeffrey A.↗

NASA NTRS2021

Measurements of Rainfall Rate, Drop Size Distribution, and Variability at Middle and Higher Latitudes: Application to the Combined DPR-GMI Algorithm

The Global Precipitation Measurement mission is a major U.S.–Japan joint mission to understand the physics of the Earth’s global precipitation as a key component of its weather, climate, and hydrological systems. The core satellite carries a dual-precipitation radar and an advanced microwave imager which provide measurements to retrieve the drop size distribution (DSD) and rain rates using a Combined Radar-Radiometer Algorithm (CORRA). Our objective is to validate key assumptions and parameterizations in CORRA and enable improved estimation of precipitation products, especially in the middle-to-higher latitudes in both hemispheres. The DSD parameters and statistical relationships between DSD parameters and radar measurements are a central part of the rainfall retrieval algorithm, which is complicated by regimes where DSD measurements are abysmally sparse (over the open ocean). In view of this, we have assembled optical disdrometer datasets gathered by research vessels, ground stations, and aircrafts to simulate radar observables and validate the scattering lookup tables used in CORRA. The joint use of all DSD datasets spans a large range of drop concentrations and characteristic drop diameters. The scaling normalization of DSDs defines an intercept parameter N(W), which normalizes the concentrations, and a scaling diameter D(m), which compresses or stretches the diameter coordinate axis. A major finding of this study is that a single relationship between N(W) and D(m), on average, unifies all datasets included, from stratocumulus to heavier rainfall regimes. A comparison with the N(W)–D(m) relation used as a constraint in versions 6 and 7 of CORRA highlights the scope for improvement of rainfall retrievals for small drops (D(m) < 1 mm) and large drops (D(m) > 2 mm). The normalized specific attenuation–reflectivity relationships used in the combined algorithm are also found to match well the equivalent relationships derived using DSDs from the three datasets, suggesting that the currently assumed lookup tables are not a major source of uncertainty in the combined algorithm rainfall estimates.

Viswanathan Bringi↗

NASA NTRS1984

Microdensitometer errors: Their effect on photometric data reduction

The performance of densitometers used for photometric data reduction of high dynamic range electrographic plate material is analyzed. Densitometer repeatability is tested by comparing two scans of one plate. Internal densitometer errors are examined by constructing histograms of digitized densities and finding inoperative bits and differential nonlinearity in the analog to digital converter. Such problems appear common to the four densitometers used in this investigation and introduce systematic algorithm dependent errors in the results. Strategies to improve densitometer performance are suggested.

Bozyan, E. P.↗

NASA NTRS2020

Dust Aerosol Retrieval Over the Oceans With the MODIS/VIIRS Dark‐Target Algorithm: 1. Dust Detection

To prepare for implementation of a new aerosol retrieval specifically designed for dust aerosol over ocean in the operational Dark-Target (DT) algorithms for the Moderate-resolution Imaging Spectrometer (MODIS) and Visible Infrared Imaging Radiometer Suite (VIIRS) satellite sensors, we focus on the challenge of detecting dust. We first survey the literature on existing dust detection algorithms and then develop an innovative algorithm that combines near-UV (deep blue), visible, and thermal infrared (TIR) wavelength spectral tests. The new detection algorithm is applied to Terra and Aqua MODIS granules and compared with other dust detection possibilities from existing MODIS products. Quantitative evaluation of the new dust detection algorithm is conducted using both a collocated AERONET-MODIS data set and collocated Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO)-MODIS data set. From comparison with both AERONET and CALIOP measurements, we estimate the new dust detection algorithm detects about 30% of weakly dusty pixels and more than 80% of heavily dusty pixels, with false detections in the range of 1–2%. The very low false detection rate is particularly noteworthy in comparison with existing literature. Compared with the dust flag currently available as part of the MODIS cloud mask product (MOD35/MYD35), and dust classification based on commonly used thresholds with aerosol optical depth (AOD) and Angstrom exponent (AE), the new dust detection algorithm finds more dusty pixels and fewer false detections.

spectral dust detection↗

NASA NTRS2006

Cloud Radiative Forcing at the ARM Climate Research Facility: Technique, Validation, and Comparison to Satellite-derived Diagnostic Quantities - Part 1

It has been hypothesized that continuous ground-based remote sensing measurements from active and passive remote sensors combined with regular soundings of the atmospheric thermodynamic structure can be combined to describe the effects of clouds on the clear sky radiation fluxes. We critically test that hypothesis in this paper and a companion paper (Part II). Using data collected at the Southern Great Plains (SGP) Atmospheric Radiation Measurement (ARM) site sponsored by the U.S. Department of Energy, we explore an analysis methodology that results in the characterization of the physical state of the atmospheric profile at time resolutions of five minutes and vertical resolutions of 90 m. The description includes thermodynamics and water vapor profile information derived by merging radiosonde soundings with ground-based data, and continues through specification of the cloud layer occurrence and microphysical and radiative properties derived from retrieval algorithms and parameterizations. The description of the atmospheric physical state includes a calculation of the infrared and clear and cloudy sky solar flux profiles. Validation of the methodology is provided by comparing the calculated fluxes with top of atmosphere (TOA) and surface flux measurements and by comparing the total column optical depths to independently derived estimates. We find over a 1-year period of comparison in overcast uniform skies, that the calculations are strongly correlated to measurements with biases in the flux quantities at the surface and TOA of less than 10% and median fractional errors ranging from 20% to as low as 2%. In the optical depth comparison for uniform overcast skies during the year 2000 where the optical depth varies over 3 orders of magnitude we find a mean positive bias of 46% with a median bias of less than 10% and a 0.89 correlation coefficient. The slope of the linear regression line for the optical depth comparison is 0.86 with a normal deviation of 20% about this line. In addition to a case study where we examine the cloud radiative effects at the TOA, surface and atmosphere by a middle latitude synoptic-scale cyclone, we examine the cloud top pressure and optical depth retrievals of ISCCP and LBTM over a period of 1 year. Using overcast period from the year 2000, we find that the satellite algorithms tend to bias cloud tops into the middle troposphere and underestimate optical depth in high optical depth events (greater than 100) by as much as a factor of 2.

Mace, Gerald G.↗

NASA NTRS1995

Optimal Signal Processing of Frequency-Stepped CW Radar Data

An optimal signal processing algorithm is derived for estimating the time delay and amplitude of each scatterer reflection using a frequency-stepped CW system. The channel is assumed to be composed of abrupt changes in the reflection coefficient profile. The optimization technique is intended to maximize the target range resolution achievable from any set of frequency-stepped CW radar measurements made in such an environment. The algorithm is composed of an iterative two-step procedure. First, the amplitudes of the echoes are optimized by solving an overdetermined least squares set of equations. Then, a nonlinear objective function is scanned in an organized fashion to find its global minimum. The result is a set of echo strengths and time delay estimates. Although this paper addresses the specific problem of resolving the time delay between the two echoes, the derivation is general in the number of echoes. Performance of the optimization approach is illustrated using measured data obtained from an HP-851O network analyzer. It is demonstrated that the optimization approach offers a significant resolution enhancement over the standard processing approach that employs an IFFT. Degradation in the performance of the algorithm due to suboptimal model order selection and the effects of additive white Gaussion noise are addressed.

Ybarra, Gary A.↗

NASA NTRS1995

Optimal Signal Processing of Frequency-Stepped CW Radar Data

An optimal signal processing algorithm is derived for estimating the time delay and amplitude of each scatterer reflection using a frequency-stepped CW system. The channel is assumed to be composed of abrupt changes in the reflection coefficient profile. The optimization technique is intended to maximize the target range resolution achievable from any set of frequency-stepped CW radar measurements made in such an environment. The algorithm is composed of an iterative two-step procedure. First, the amplitudes of the echoes are optimized by solving an overdetermined least squares set of equations. Then, a nonlinear objective function is scanned in an organized fashion to find its global minimum. The result is a set of echo strengths and time delay estimates. Although this paper addresses the specific problem of resolving the time delay between the first two echoes, the derivation is general in the number of echoes. Performance of the optimization approach is illustrated using measured data obtained from an HP-X510 network analyzer. It is demonstrated that the optimization approach offers a significant resolution enhancement over the standard processing approach that employs an IFFT. Degradation in the performance of the algorithm due to suboptimal model order selection and the effects of additive white Gaussion noise are addressed.

Ybarra, Gary A.↗

NASA NTRS2008

Volume Averaged Height Integrated Radar Reflectivity (VAHIRR) Cost-Benefit Analysis

Lightning Launch Commit Criteria (LLCC) are designed to prevent space launch vehicles from flight through environments conducive to natural or triggered lightning and are used for all U.S. government and commercial launches at government and civilian ranges. They are maintained by a committee known as the NASA/USAF Lightning Advisory Panel (LAP). The previous LLCC for anvil cloud, meant to avoid triggered lightning, have been shown to be overly restrictive. Some of these rules have had such high safety margins that they prohibited flight under conditions that are now thought to be safe 90% of the time, leading to costly launch delays and scrubs. The LLCC for anvil clouds was upgraded in the summer of 2005 to incorporate results from the Airborne Field Mill (ABFM) experiment at the Eastern Range (ER). Numerous combinations of parameters were considered to develop the best correlation of operational weather observations to in-cloud electric fields capable of rocket triggered lightning in anvil clouds. The Volume Averaged Height Integrated Radar Reflectivity (VAHIRR) was the best metric found. Dr. Harry Koons of Aerospace Corporation conducted a risk analysis of the VAHIRR product. The results indicated that the LLCC based on the VAHIRR product would pose a negligible risk of flying through hazardous electric fields. Based on these findings, the Kennedy Space Center Weather Office is considering seeking funding for development of an automated VAHIRR algorithm for the new ER 45th Weather Squadron (45 WS) RadTec 431250 weather radar and Weather Surveillance Radar-1988 Doppler (WSR-88D) radars. Before developing an automated algorithm, the Applied Meteorology Unit (AMU) was tasked to determine the frequency with which VAHIRR would have allowed a launch to safely proceed during weather conditions otherwise deemed "red" by the Launch Weather Officer. To do this, the AMU manually calculated VAHIRR values based on candidate cases from past launches with known anvil cloud LLCC violations. An automated algorithm may be developed if the analyses from past launches show VAHIRR would have provided a significant cost benefit by allowing a launch to proceed. The 45 WS at the ER and 30th Weather Squadron (30 WS) at the Western Range provided the AMU with launch weather summaries from past launches that were impacted by LLCC. The 45 WS provided summaries from 14 launch attempts and the 30 WS fkom 5. The launch attempts occurred between December 2001 and June 2007. These summaries helped the AMU determine when the LLCC were "red" due to anvil cloud. The AMU collected WSR-88D radar reflectivity, cloud-to-ground lightning strikes, soundings and satellite imagery. The AMU used step-by-step instructions for calculating VAHIRR manually as provided by the 45 WS. These instructions were used for all of the candidate cases when anvil cloud caused an LLCC violation identified in the launch weather summaries. The AMU evaluated several software programs capable of visualizing radar data so that VAHIRR could be calculated and chose GR2Analyst from Gibson Ridge Software, LLC. Data availability and lack of detail from some launch weather summaries permitted analysis of six launch attempts from the ER and none from the WR. The AMU did not take into account whether or not other weather LCC violations were occurring at the same time as the anvil cloud LLCC since the goal of this task was to determine how often VAHIRR provided relief to the anvil cloud LLCC at any time during several previous launch attempts. Therefore, in the statistics presented in this report, it is possible that even though VAHIRR provided relief to the anvil cloud LLCC, other weather LCC could have been violated not permitting the launch to proceed. The results of this cost-benefit analysis indicated VAHIRR provided relief from the anvil cloud LLCC between about 15% and 18% of the time for varying 5-minute time periods based on summaries fkom six launch attempts and would have allowed launch to proceed that were otherwise "NO GO" due to the anvil cloud LLCC if the T-0 time occurred during the anvil cloud LLCC violations.

Bauman, William H., III↗

NASA NTRS2011

The RHESSI Microflare Height Distribution

We present the first in-depth statistical survey of flare source heights observed by RHESSI. Flares were found using a flare-finding algorithm designed to search the 6-10 keV count-rate when RHESSI's full sensitivity was available in order to find the smallest events (Christe et al., 2008). Between March 2002 and March 2007, a total of 25,006 events were found. Source locations were determined in the 4-10 keV, 10-15 keV, and 15-30 keV energy ranges for each event. In order to extract the height distribution from the observed projected source positions, a forward-fit model was developed with an assumed source height distribution where height is measured from the photosphere. We find that the best flare height distribution is given by g (h) oc exp(-h/lambda) where lambda = 6.1 plus or minus 0.3 Mm is the scale height. A power law height distribution with a negative power law index, gamma = 3.1 plus or minus 0.3 is also consistent with the data. Interpreted as thermal loop top sources, these heights are compared to loops generated by a potential field model (PFSS). The measured flare heights distribution are found to be much steeper than the potential field loop height distribution which may be a signature of the flare energization process.

Christe, P.↗

NASA NTRS2011

Hazard Detection Software for Lunar Landing

The Autonomous Landing and Hazard Avoidance Technology (ALHAT) Project is developing a system for safe and precise manned lunar landing that involves novel sensors, but also specific algorithms. ALHAT has selected imaging LIDAR (light detection and ranging) as the sensing modality for onboard hazard detection because imaging LIDARs can rapidly generate direct measurements of the lunar surface elevation from high altitude. Then, starting with the LIDAR-based Hazard Detection and Avoidance (HDA) algorithm developed for Mars Landing, JPL has developed a mature set of HDA software for the manned lunar landing problem. Landing hazards exist everywhere on the Moon, and many of the more desirable landing sites are near the most hazardous terrain, so HDA is needed to autonomously and safely land payloads over much of the lunar surface. The HDA requirements used in the ALHAT project are to detect hazards that are 0.3 m tall or higher and slopes that are 5 or greater. Steep slopes, rocks, cliffs, and gullies are all hazards for landing and, by computing the local slope and roughness in an elevation map, all of these hazards can be detected. The algorithm in this innovation is used to measure slope and roughness hazards. In addition to detecting these hazards, the HDA capability also is able to find a safe landing site free of these hazards for a lunar lander with diameter .15 m over most of the lunar surface. This software includes an implementation of the HDA algorithm, software for generating simulated lunar terrain maps for testing, hazard detection performance analysis tools, and associated documentation. The HDA software has been deployed to Langley Research Center and integrated into the POST II Monte Carlo simulation environment. The high-fidelity Monte Carlo simulations determine the required ground spacing between LIDAR samples (ground sample distances) and the noise on the LIDAR range measurement. This simulation has also been used to determine the effect of viewing on hazard detection performance. The software has also been deployed to Johnson Space Center and integrated into the ALHAT real-time Hardware-in-the-Loop testbed.

Huertas, Andres↗

NASA NTRS1980

Microwave radiometric determination of oceanographic and meteorological parameters

The thermal microwave brightness from the atmosphere over an ocean in the range 5-40 GHz is influenced primarily by the distribution of vapor and liquid water in the atmosphere and the temperature and wind speed at the sea surface. The Scanning Multichannel Microwave Radiometer (SMMR), which was carried aboard both the Nimbus-7 and Seasat satellites (both launched in 1978), measures this radiation at five frequencies to find these four parameters. A retrieval algorithm has been developed which, on simulated data, yields accuracies of 1.5 C in sea surface temperature, 0.9 m/s in wind speed, 4 mg/ sq cm of cloud liquid water content and 0.14gm/sq cm of precipitable water vapor. Results from the Seasat SMMR, while both preliminary and sparse, are consistent with these simulations.

Wilheit, T. T.↗

NASA NTRS1987

Algorithm Sorts Groups Of Data

For efficient sorting, algorithm finds set containing minimum or maximum most significant data. Sets of data sorted as desired. Sorting process simplified by reduction of each multielement set of data to single representative number. First, each set of data expressed as polynomial with suitably chosen base, using elements of set as coefficients. Most significant element placed in term containing largest exponent. Base selected by examining range in value of data elements. Resulting series summed to yield single representative number. Numbers easily sorted, and each such number converted back to original set of data by successive division. Program written in BASIC.

Evans, J. D.↗

NASA NTRS1998

Development of Algorithms and Error Analyses for the Short Baseline Lightning Detection and Ranging System

NASA, at the John F. Kennedy Space Center (KSC), developed and operates a unique high-precision lightning location system to provide lightning-related weather warnings. These warnings are used to stop lightning- sensitive operations such as space vehicle launches and ground operations where equipment and personnel are at risk. The data is provided to the Range Weather Operations (45th Weather Squadron, U.S. Air Force) where it is used with other meteorological data to issue weather advisories and warnings for Cape Canaveral Air Station and KSC operations. This system, called Lightning Detection and Ranging (LDAR), provides users with a graphical display in three dimensions of 66 megahertz radio frequency events generated by lightning processes. The locations of these events provide a sound basis for the prediction of lightning hazards. This document provides the basis for the design approach and data analysis for a system of radio frequency receivers to provide azimuth and elevation data for lightning pulses detected simultaneously by the LDAR system. The intent is for this direction-finding system to correct and augment the data provided by LDAR and, thereby, increase the rate of valid data and to correct or discard any invalid data. This document develops the necessary equations and algorithms, identifies sources of systematic errors and means to correct them, and analyzes the algorithms for random error. This data analysis approach is not found in the existing literature and was developed to facilitate the operation of this Short Baseline LDAR (SBLDAR). These algorithms may also be useful for other direction-finding systems using radio pulses or ultrasonic pulse data.

Starr, Stanley O.↗