ALBERT

Description: A one-speed Boltzmann transport theory, with diffusion approximations, is applied to study the radiative transfer properties of lightning in optically thick thunderclouds. Near-infrared (lambda = 0.7774 micrometers) photons associated with a prominent oxygen emission triplet in the lightning spectrum are considered. Transient and spatially complex lightning radiation sources are placed inside a rectangular parallelepiped thundercloud geometry and the effects of multiple scattering are studied. The cloud is assumed to be composed of a homogeneous collection of identical spherical water droplets, each droplet a nearly conservative, anisotropic scatterer. Conceptually, we treat the thundercloud like a nuclear reactor, with photons replaced by neutrons, and utilize standard one-speed neutron diffusion techniques common in nuclear reactor analyses. Valid analytic results for the intensity distribution (expanded in spherical harmonics) are obtained for regions sufficiently far from sources. Model estimates of the arrival-time delay and pulse width broadening of lightning signals radiated from within the cloud are determined and the results are in good agreement with both experimental data and previous Monte Carlo estimates. Additional model studies of this kind will be used to study the general information content of cloud top lightning radiation signatures.

Description: An aircraft locally distorts the ambient thundercloud electric field. In order to determine the field in the absence of the aircraft, an aircraft calibration is required. In this work a matrix inversion method is introduced for calibrating an aircraft equipped with four or more electric field sensors and a high-voltage corona point that is capable of charging the aircraft. An analytic, closed form solution for the estimate of a (3 x 3) aircraft calibration matrix is derived, and an absolute calibration experiment is used to improve the relative magnitudes of the elements of this matrix. To demonstrate the calibration procedure, we analyze actual calibration date derived from a Lear jet 28/29 that was equipped with five shutter-type field mill sensors (each with sensitivities of better than 1 V/m) located on the top, bottom, port, starboard, and aft positions. As a test of the calibration method, we analyze computer-simulated calibration data (derived from known aircraft and ambient fields) and explicitly determine the errors involved in deriving the variety of calibration matrices. We extend our formalism to arrive at an analytic solution for the ambient field, and again carry all errors explicitly.

Description: A new method is introduced for inferring the charges deposited in a lightning flash. Lightning-caused field changes (delta E's) are described by a more general volume charge distribution than is defined on a large cartesian grid system centered above the measuring networks. It is shown that a linear system of equations can be used to relate delta E's at the ground to the values of charge on this grid. It is possible to apply more general physical constraints to the charge solutions, and it is possible to access the information content of the delta E data. Computer-simulated delta E inversions show that the location and symmetry of the charge retrievals are usually consistent with the known test sources.

Description: The Lagrange multiplier theory developed in Part I of this study is applied to complete a relative calibration of a Citation aircraft that is instrumented with six field mill sensors. When side constraints related to average fields are used, the Lagrange multiplier method performs well in computer simulations. For mill measurement errors of 1 V m(sup -1) and a 5 V m(sup -1) error in the mean fair-weather field function, the 3D storm electric field is retrieved to within an error of about 12%. A side constraint that involves estimating the detailed structure of the fair-weather field was also tested using computer simulations. For mill measurement errors of 1 V m(sup -l), the method retrieves the 3D storm field to within an error of about 8% if the fair-weather field estimate is typically within 1 V m(sup -1) of the true fair-weather field. Using this type of side constraint and data from fair-weather field maneuvers taken on 29 June 2001, the Citation aircraft was calibrated. Absolute calibration was completed using the pitch down method developed in Part I, and conventional analyses. The resulting calibration matrices were then used to retrieve storm electric fields during a Citation flight on 2 June 2001. The storm field results are encouraging and agree favorably in many respects with results derived from earlier (iterative) techniques of calibration.

Description: A constrained, least-squares method for analyzing multiple-station measurements of lightning field changes (delta Es) is introduced. Previous methods have attempted to fit the spatial pattern of lightning delta Es using nonlinear models, such as a point charge (Q) or a point dipole (P) model. With the linear method, the delta Es are described not by models but by a general volume charge distribution that is deposited on a large (40 x 40 x 20 cu km) Cartesian grid above the measuring network. A linear system of equations is used to relate the measured delta Es to the charges that are deposited at each grid point. With this approach, the information content of the measurements can be quantified by an eigenanalysis of the covariance matrix of the linear system. Constraints can be used to reduce the infinity of possible solutions to the linear system and also to reduce systematic biases that can be introduced by the method of solution. It is shown that a Landweber iterative method, derived from the general method of steepest descent, can be used to solve the linear system and that the resulting volume charge distributions are generally consistent with computer-simulated charge sources, when these sources are over the measuring network. The Landweber iteration has also provided solutions for natural lightning events that are consistent with Q- and P-model results.

Description: No abstract available

Description: A survey of some interesting mathematical inversion studies dealing with radio, optical, and electrostatic measurements of lightning are presented. A discussion of why NASA is interested in lightning, what specific physical properties of lightning are retrieved, and what mathematical techniques are used to perform the retrievals are discussed. In particular, a relatively new multi-station VHF time-of-arrival (TOA) antenna network is now on-line in Northern Alabama and will be discussed. The network, called the Lightning Mapping Array (LMA), employs GPS timing and detects VHF radiation from discrete segments (effectively point emitters) that comprise the channel of lightning strokes within cloud and ground flashes. The LMA supports on-going ground-validation activities of the low Earth orbiting Lightning Imaging Sensor (LIS) satellite developed at NASA Marshall Space Flight Center (MSFC) in Huntsville, Alabama. The LMA also provides detailed studies of the distribution and evolution of thunderstorms and lightning in the Tennessee Valley, and offers interesting comparisons with other meteorological/geophysical datasets. In order to take full advantage of these benefits, it is essential that the LMA channel mapping accuracy (in both space and time) be fully characterized and optimized. A new channel mapping retrieval algorithm is introduced for this purpose. To characterize the spatial distribution of retrieval errors, the algorithm has been applied to analyze literally tens of millions of computer-simulated lightning VHF point sources that have been placed at various ranges, azimuths, and altitudes relative to the LMA network. Statistical results are conveniently summarized in high-resolution, color-coded, error maps.

Description: Over two decades, the NASA Marshall Space Flight Center, the University of Alabama in Huntsville, and their partners have demonstrated the effectiveness and value of space-based lightning observations as a remote sensing tool for Earth science research and applications, and, in the process, established a robust global lightning climatology. The Lightning Imaging Sensor (LIS) on the Tropical Rainfall Measuring Mission (TRMM) provided global observations of tropical lightning for an impressive 17 years before that mission came to a close in April 2015. Now a space-qualified LIS, built as the flight spare for TRMM, has been installed on the International Space Station (ISS) for a minimum two year mission following its SpaceX launch on February 19, 2017. The LIS, flown as a hosted payload on the Department of Defense Space Test Program-Houston 5 (STP-H5) mission, was delivered to the ISS in the Dragon trunk and robotically installed in an Earth-viewing position on the outside of the ISS. Following successful activation and checkout, LIS has continuously observed the amount, rate, and radiant energy lightning within its field-of-view as it orbits the Earth. Placing LIS on the Space Station provides a great opportunity to not only extend the 17-year TRMM LIS record of tropical lightning measurements but also to expand that coverage to higher latitudes missed by the previous mission. Furthermore, this mission continues the important science focus to better understand the processes which cause lightning, as well as the connections between lightning and subsequent severe weather events. This understanding is a key to improving weather predictions and saving lives and property here in the United States and around the world. The LIS measurements, along with observations from the new Geostationary Lightning Mapper (GLM) operating on NOAA's newest weather satellites, the Geosynchronous Operational Environmental Satellite-16/17 (GOES-16/17), are being used to cross-validate both systems. An especially unique contribution from the ISS platform is the production of real-time lightning data, especially valuable for operational forecasting and warning applications over data sparse regions such as the oceans. Finally, LIS provides simultaneous and complementary observations with other ISS payloads such as the European Space Agency's Atmosphere-Space Interaction Monitor (ASIM) that is exploring the connection between thunderstorms and lightning with terrestrial gamma-ray flashes (TGFs). Leveraging TRMM's well-established processing and data handling assures that LIS data can be quickly delivered to users.

Description: The Geostationary Operational Environmental Satellite -16 (GOES-16) Geostationary Lightning Mapper (GLM) is evaluated for many months during the Post Launch Product Test (PLPT) phase in order to ensure that optimal products are available for both the operational forecasting and broader scientific research communities. The emphasis of the PLPT phase is to validate the GLM performance (i.e., lightning flash detection efficiency, geolocation and time-stamp accuracy) using an extensive network of independent ground-based, in-situ, and space-based reference lightning detection systems. However, another essential aspect of the PLPT phase is to obtain benchmarks of the GLM lightning optical amplitude, so that any long-term degradation in the nadir-staring GLM camera system can be realized and quantitatively assessed. This is accomplished in a straight-forward manner by collecting a very large sample of lightning flashes across many geographical regions in the GLM field-of-view so that statistically meaningful benchmarks of lightning optical amplitude (i.e., optical energy in units of femto-joules per flash) are obtained. The benchmarking is particularly important to follow-on studies that will attempt to incorporate the flash optical energy product into new derived products (e.g., energy-weighted lightning "jump" warning algorithms, and lightning nitrogen oxides production estimates).

Description: The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error plots are provided for both the simulations and actual data analyses.