North Alabama Lightning Mapping Array (LMA): VHF Source Retrieval Algorithm and Error Analyses (original) (raw)
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Error Analyses of the North Alabama Lightning Mapping Array (LMA)
Two approaches are used to characterize how accurately the North Alabama Lightning Mapping Array (LMA) is able to locate lightning VHF sources in space and in time. The first method uses a Monte Carlo computer simulation to estimate source retrieval errors. The simulation applies a VHF source retrieval algorithm that was recently developed at the NASA-MSFC and that is similar, but not identical to, the standard New Mexico Tech retrieval algorithm. The second method uses a purely theoretical technique (i.e., chi-squared Curvature Matrix theory) to estimate retrieval errors. Both methods assume that the LMA system has an overall rms timing error of 50ns, but all other possible errors (e.g., multiple sources per retrieval attempt) are neglected. The detailed spatial distributions of retrieval errors are provided. Given that the two methods are completely independent of one another, it is shown that they provide remarkably similar results, except that the chi-squared theory produces lar...
On the retrieval of lightning radio sources from time-of-arrival data
Journal of Geophysical Research, 1996
We examine the problem of retrieving three-dimensional lightning locations from radio frequency time-of-arrival (TOA) measurements. Arbitrary antenna locations are considered. By judiciously differencing measurements that are related to the location of the antennas and their excitation times, the problem is converted from the initial spherical nonlinear form to a system of linear equations. In the linear formalism, the source location and time-of-occurrence is viewed geometrically as an intersection of hyperplanes in the four-dimensional Minkowski space (x,y, z, t). The linear equations are solved to obtain explicit analytic expressions for the location and time variables. Retrieval errors are not interpreted with conventional Geometrical Dilution of Precision (GDOP) arguments as discussed by Holmes and Reedy [ 1951], but with more recent inversion analyses considered by Twomey [ 1977]. Measurement errors are propagated analytically so that the specific effect of these errors on the solution is clarified. The sensitivity of the solution on the number of antennas used, antenna network geometry, source position, and measurement differencing schemes are discussed in terms of the eigenvalues of the linear system. 1. Introduction A variety of data analysis techniques and hardware have been used in the retrieval of lightning locations from ground-based radio frequency time-of-arrival (TEA) measurements [Holmes and Reedy, 1951; Lewis et al., 1960; Oetzel and Pierce, 1969; Proctor, 1971; Cianos et al. , 1972; Murty and MacClement , 1973; MacClement and Murty, 1978; Taylor, 1978; Rustan et al., 1980; Bent et al., 1983; Thomson et al., 1994; and Hager and . Primary differences between these studies include the number and type of antennas used, the antenna baseline, whether a two-dimensional or three-dimensional fix of the source is desired, the mathematical means for retrieving source location, and the procedure for estimating retrieval error.
On-orbit direction finding of lightning radio frequency emissions recorded by the FORTE satellite
Radio Science, 2002
1] The recording of radio frequency signals from space potentially provides a means for global, near-real-time remote sensing of vigorous convective storms and a possible early warning system for convection-associated severe weather. In general, radio frequency signals arriving at a satellite with modest antenna gain do not directly reveal the ground location of those signals' source. We develop here a means of inferring the source location using repeated signal recordings from the same source storm, with the successive recordings taken along a significant segment of the satellite pass in view of the storm. The method is based on the ratio of received power on each of a pair of crossed dipole antennas. This method has a positional accuracy of 100-500 km. Moreover, the method has an intrinsic right-left (with respect to the subsatellite track) location ambiguity. A promising use of this technique in future applications will be as an aid in assigning lightning RF emission sources to meteorological features from other global remote-sensing products, for example satellite infrared imagery of clouds.
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...
3-Dimensional Lightning Observations Using a Time-of-Arrival Lightning Mapping System
SAE Technical Paper Series, 2001
A lightning mapping system has been developed that locates the sources of VHF radiation from lightning discharges in three spatial dimensions and time. The system consists of several VHF receivers distributed over an area of about 100 km diameter. The system locates VHF radiation sources over the array with an accuracy of about 100 m. The system locates sources out to 250 km from the center of the array with reduced accuracy. The observations are found to reflect the basic charge structure of electrified storms.
2016
The World Wide Lighting Location Network (WWLLN) locates lightning globally, using sparsely dis-tributed very low frequency (VLF) detection stations. Due to WWLLN’s detection at VLF (in this case10 kHz), the lightning signals from strong strokes can propagate up to 104 km to WWLLN sensors and still be suitable for triggering a station. A systematic evaluation of the performance of WWLLN is undertaken, using a higher-frequency (0–500 kHz) detection array [the Los Alamos Sferic Array (LASA)] as a ground truth during an entire thunderstorm season in a geographically confined case study in Florida. It is found that (a) WWLLN stroke-detection efficiency rises sharply to several percent as the estimated lightning current amplitude surpasses30 kA; (b) WWLLN spatial accuracy is around 15 km, good enough to resolve convective-storm cells within a larger storm complex; (c) WWLLN is able to detect intracloud and cloud-to-ground discharges with comparable efficiency, as long as the current is c...
Accuracy of the Lightning Mapping Array
Journal of Geophysical Research, 2004
1] The location accuracy of the New Mexico Tech Lightning Mapping Array (LMA) has been investigated experimentally using sounding balloon measurements, airplane tracks, and observations of distant storms. We have also developed simple geometric models for estimating the location uncertainty of sources both over and outside the network. The model results are found to be a good estimator of the observed errors and also agree with covariance estimates of the location uncertainties obtained from the least squares solution technique. Sources over the network are located with an uncertainty of 6-12 m rms in the horizontal and 20-30 m rms in the vertical. This corresponds well with the uncertainties of the arrival time measurements, determined from the distribution of chi-square values to be 40-50 ns rms. Outside the network the location uncertainties increase with distance. The geometric model shows that the range and altitude errors increase as the range squared, r 2 , while the azimuthal error increases linearly with r. For the 13 station, 70 km diameter network deployed during STEPS the range and height errors of distant sources were comparable to each other, while the azimuthal errors were much smaller. The difference in the range and azimuth errors causes distant storms to be elongated radially in plan views of the observations. The overall results are shown to agree well with hyperbolic formulations of time of arrival measurements [e.g., Proctor, 1971]. Two appendices describe (1) the basic operation of the LMA and the detailed manner in which its measurements are processed and (2) the effect of systematic errors on lightning observations. The latter provides an alternative explanation for the systematic height errors found by in distant storm data from the Lightning Detection and Ranging system at Kennedy Space Center.
Journal of Atmospheric and Oceanic Technology, 2007
A "dimensional reduction" ("DR") method is introduced for analyzing lightning field changes (⌬Es) whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight (x, y, z, Q, xЈ, yЈ, zЈ, QЈ) to just four (x, y, z, Q). The four unknowns (x, y, z, Q) are found by performing a numerical minimization of a chi-square function. At each step of the minimization, an overdetermined fixed matrix (OFM) method is used to immediately retrieve the best "residual source" (xЈ, yЈ, zЈ, QЈ), given the values of (x, y, z, Q). In this way, all eight parameters (x, y, z, Q, xЈ, yЈ, zЈ, QЈ) are found, yet a numerical search of only four parameters (x, y, z, Q) is required. The DR method has been used to analyze lightningcaused ⌬Es derived from multiple ground-based electric field measurements at the NASA Kennedy Space Center (KSC) and U.S. Air Force Eastern Range (ER). The accuracy of the DR method has been assessed by comparing retrievals with data provided by the lightning detection and ranging (LDAR) system at the KSC-ER, and from least squares error estimation theory, and the method is shown to be a useful "stand alone" charge retrieval tool. Since more than one charge distribution describes a finite set of ⌬Es (i.e., solutions are nonunique), and since there can be appreciable differences in the physical characteristics of these solutions, not all DR solutions are physically acceptable. Hence, an alternative and more accurate method of analysis is introduced that uses LDAR data to constrain the geometry of the charge solutions, thereby removing physically unacceptable retrievals. The charge solutions derived from this method are shown to compare well with independent satellite-and ground-based observations of lightning in several Florida storms.
Journal of Atmospheric and Oceanic Technology, 2006
The World Wide Lighting Location Network (WWLLN) locates lightning globally, using sparsely distributed very low frequency (VLF) detection stations. Due to WWLLN’s detection at VLF (in this case ∼10 kHz), the lightning signals from strong strokes can propagate up to ∼104 km to WWLLN sensors and still be suitable for triggering a station. A systematic evaluation of the performance of WWLLN is undertaken, using a higher-frequency (0–500 kHz) detection array [the Los Alamos Sferic Array (LASA)] as a ground truth during an entire thunderstorm season in a geographically confined case study in Florida. It is found that (a) WWLLN stroke-detection efficiency rises sharply to several percent as the estimated lightning current amplitude surpasses ∼30 kA; (b) WWLLN spatial accuracy is around 15 km, good enough to resolve convective-storm cells within a larger storm complex; (c) WWLLN is able to detect intracloud and cloud-to-ground discharges with comparable efficiency, as long as the current ...
Dependency of VHF broad band lightning source mapping on Fourier spectra
Geophysical Research Letters, 2000
In the VHF broad band interferometer, the Fourier transform is applied to analyze the whole frequency range of lightning radiation sources. The position of a radiation source can be determined by resolving the incident angle for each frequency component against at least three-antenna sensors, and then by averaging the incident angles of all frequency components the angular position can be located. This arithmetic-averaging method as proposed by previous authors has a disadvantage, especially for cloud-to-ground flashes, that is positions of lightning leader channels near ground level can not be mapped well. It is found that Fourier spectral amplitudes of broad band pulses decrease with increasing frequency, and frequency components having low spectral amplitudes give less contribution to the lightning mapping. To improve the mapping, a weighted-averaging method is proposed. The method provides a way to minimize the influence of frequency components, which contribute less to the lightning mapping.