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: 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: Each year, thousands of lightning electric field disturbances are recorded and archived by the ground-based field mill (FM) network at the NASA Kennedy Space Center (KSC) and USAF Eastern Range (ER). The FM network has a range of several tens of kilometers, and a digital accuracy of 4 V/m. It has provided years of continuous lightning warning surveillance to KSC-ER space vehicle launch operations, and has undergone one major hardware upgrade since its inception in the early 1970s. Additional KSC lightning warning data is derived from a multistation radio time-of-arrival system called Lightning Detection and Ranging (LDAR). This system provides the location and space-time mapping of individual lightning channels (for both cloud and ground flashes). Additional lightning information for the KSC region is available from the National Lightning Detection Network (NLDN) and a 5-station local magnetic direction finder network. In this study, all of the above mentioned data are used to ground-validate data derived from the Lightning Imaging Sensor (LIS) onboard the Tropical Rainfall Measuring Mission (TRMM). The FM network can be used to retrieve the charges deposited in a lightning flash, provided the flash is within a few kilometers of the FM Network. Although it is rare to obtain a TRMM overpass of thunderstorms hat occur this close to the FM network, seven such storms have been found and examined in this study. We compare the times and locations of LIS optical pulses with the spatial-temporal character of the FM, LDAR, and magnetic direction finder data. We also inter-compare LIS optical pulse amplitude data with FM-derived charge magnitudes, number of LDAR radio sources, and peak current values from magnetic direction finder data. Generally speaking, LIS lightning locations and times agree favorably with the KSC ground-based systems for most cases, but little correlation appears to exist between optical pulse amplitude and any of charge, # LDAR sources, peak current), owing possibly to the effects of source complexity and/or cloud multiple scattering.

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: 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: A new multi-station VHF time-of-arrival (TOA) antenna network is, at the time of this writing, coming on-line in Northern Alabama. 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 network will support 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. It will also provide for many interesting and detailed studies of the distribution and evolution of thunderstorms and lightning in the Tennessee Valley, and will offer many interesting comparisons with other meteorological/geophysical wets associated with lightning and thunderstorms. 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. In this study, a new revised channel mapping retrieval algorithm is introduced. The algorithm is an extension of earlier work provided in Koshak and Solakiewicz (1996) in the analysis of the NASA Kennedy Space Center (KSC) Lightning Detection and Ranging (LDAR) system. As in the 1996 study, direct algebraic solutions are obtained by inverting a simple linear system of equations, thereby making computer searches through a multi-dimensional parameter domain of a Chi-Squared function unnecessary. However, the new algorithm is developed completely in spherical Earth-centered coordinates (longitude, latitude, altitude), rather than in the (x, y, z) cartesian coordinates employed in the 1996 study. Hence, no mathematical transformations from (x, y, z) into spherical coordinates are required (such transformations involve more numerical error propagation, more computer program coding, and slightly more CPU computing time). The new algorithm also has a more realistic definition of source altitude that accounts for Earth oblateness (this can become important for sources that are hundreds of kilometers away from the network). In addition, the new algorithm is being applied to analyze computer simulated LMA datasets in order to obtain detailed location/time retrieval error maps for sources in and around the LMA network. These maps will provide a more comprehensive analysis of retrieval errors for LMA than the 1996 study did of LDAR retrieval errors. Finally, we note that the new algorithm can be applied to LDAR, and essentially any other multi-station TWA network that depends on direct line-of-site antenna excitation.

Description: The Optical Transient Detector (OTD) is a space-based instrument specifically designed to detect and locate lightning discharges as it orbits the Earth. This instrument is a scientific payload on the MicroLab-1 satellite that was launched into a low-earth, 70 deg. inclination orbit in April 1995. Given the orbital trajectory of the satellite, most regions of the earth are observed by the OTD instrument more than 400 times during a one year period, and the average duration of each observation is 2 minutes. The OTD instrument optically detects lightning flashes that occur within its 1300x1300 sq km field-of-view during both day and night conditions. A statistical examination of OTD lightning data reveals that nearly 1.4 billion flashes occur annually over the entire earth. This annual flash count translates to an average of 44 +/- 5 lightning flashes (intracloud and cloud-to-ground combined) occurring around the globe every second, which is well below the traditional estimate of 100 flashes per second that was derived in 1925 from world thunder-day records. The range of uncertainty for the OTD global totals represents primarily the uncertainty (and variability) in the flash detection efficiency of the instrument. The OTD measurements have been used to construct lightning climatology maps that demonstrate the geographical and seasonal distribution of lightning activity for the globe. An analysis of this annual lightning distribution confirms that lightning occurs mainly over land areas, with an average land:ocean ratio of 10:1. A dominant Northern Hemisphere summer peak occurs in the annual cycle, and evidence is found for a tropically-driven semiannual cycle.

Description: Laboratory calibration and observed background radiance data are used to determine the effective sensitivities of the Optical Transient Detector and Lightning Imaging Sensor, as functions of local hour and pixel location within the instrument arrays. The effective LIS thresholds, expressed as radiances emitted normal to cloud top, are 4.0 plus or minus 0.7 and 7.6 plus or minus 3.3 micro J/ster/m (sup 2) for night and local noon; the OTD thresholds am 11.7 plus or minus 2.2 and 16.8 plus or minus 4.6 microJ/ster/m (sup 2). LIS and OTD minimum signal to noise ratios occur from 0800 to 1600 local time, and attain values of 10 plus or minus 2 and 20 plus or minus 3, respectively. False alarm rate due to instrument noise yields approximately 5 false triggers per month for LIS, and is negligible for OTD. Flash detection efficiency, based on prior optical pulse sensor measurements, is predicted to be 93 plus or minus 4% and 73 plus or minus 11% for LIS night and noon; 56 plus or minus 7% and 44 plus or minus 9% for OTD night and noon, corresponding to a 12 - 20% diurnal variability and LIS:OTD ratio of 1.7. Use of the weighted daily mean detection efficiency (i.e., not controlling for local hour) corresponds to a sigma = 8 - 9% uncertainty. These are likely overestimates of actual flash detection efficiency due to differences in pixel ground field-of-view across the instrument arrays, which are not accounted for in the validation optical pulse sensor data.