ALBERT

Description: It is by no means a simple task to retrieve storm electric fields from an aircraft instrumented with electric field mill sensors. The presence of the aircraft distorts the ambient field in a complicated way. Before retrievals of the storm field can be made, the field mill measurement system must be "calibrated". In other words, a relationship between impressed (i.e., ambient) electric field and mill output must be established. If this relationship can be determined, it is mathematically inverted so that ambient field can be inferred from the mill outputs. Previous studies have primarily focused on linear theories where the relationship between ambient field and mill output is described by a "calibration matrix" M. Each element of the matrix describes how a particular component of the ambient field is enhanced by the aircraft. For example the product M(sub ix), E(sub x), is the contribution of the E(sub x) field to the i(th) mill output. Similarly, net aircraft charge (described by a "charge field component" E(sub q)) contributes an amount M(sub iq)E(sub q) to the output of the i(th) sensor. The central difficulty in obtaining M stems from the fact that the impressed field (E(sub x), E(sub y), E(sub z), E(sub q) is not known but is instead estimated. Typically, the aircraft is flown through a series of roll and pitch maneuvers in fair weather, and the values of the fair weather field and aircraft charge are estimated at each point along the aircraft trajectory. These initial estimates are often highly inadequate, but several investigators have improved the estimates by implementing various (ad hoc) iterative methods. Unfortunately, none of the iterative methods guarantee absolute convergence to correct values (i.e., absolute convergence to correct values has not been rigorously proven). In this work, the mathematical problem is solved directly by analytic means. For m mills installed on an arbitrary aircraft, it is shown that it is possible to solve for a single 2m-vector that provides all other needed variables (i.e., the unknown fair weather field, the unknown aircraft charge, and the unknown matrix M). Numerical tests of the solution, effects of measurement errors, and studies of solution non-uniqueness are ongoing as of this writing.

Description: No abstract available

Description: No abstract available

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 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.

Description: No abstract available

Description: A Bayesian inversion method is introduced for retrieving the fraction of ground flashes in a set of N lightning observed by a satellite lightning imager (such as the Geostationary Lightning Mapper, GLM). An exponential model is applied as a physically reasonable constraint to describe the measured lightning optical parameter distributions. Population statistics (i.e., the mean and variance) are invoked to add additional constraints to the retrieval process. The Maximum A Posteriori (MAP) solution is employed. The approach is tested by performing simulated retrievals, and retrieval error statistics are provided. The approach is feasible for N greater than 2000, and retrieval errors decrease as N is increased.

Description: No abstract available

Description: No abstract available