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: The Lightning Imaging Sensor (LIS) is a NASA Earth Observing System (EOS) instrument on the Tropical Rainfall Measuring Mission (TRMM) platform designed to acquire and investigate the distribution and variability of total lightning (i.e., cloud-to-ground and intracloud) between q35' in latitude. Since lightning is one of the responses of the atmosphere to thermodynamic and dynamic forcing, the LIS data is being used to detect deep convection without land-ocean bias, estimate the precipitation mass in the mixed phased region of thunderclouds, and differentiate storms with strong updrafts from those with weak vertical motion.

Description: The Optical Transient Detector (OTD) is a space-based instrument specifically designed to detect and locate lightning discharges (intracloud and cloud-to-ground) as it orbits the Earth. A statistical examination of OTD lightning data reveals that nearly 1.2 billion flashes occurred over the entire earth during the one year period from September 1995 through August 1996. This translates to an average of 37 lightning flashes occurring around the globe every second, which is well below the traditional estimate of 100 flashes per second. An average of 75% of the global lightning activity during the year occurs between 30' S and 30' N. An analysis of the annual lightning distribution reveals that an average of 82% of the lightning flashes occur over the continents and 18% over the oceans, which translates to an average land-ocean flash density ratio of nearly 11.

Description: The mapping of the lightning optical pulses detected by the Lightning Imaging Sensor (LIS) is compared with the radiation sources by Lightning Detection and Ranging (LDAR) and the National Lightning Detection Network (NLDN) for three thunderstorms observed during and overpasses on 15 August 1998. The comparison involves 122 flashes including 42 ground and 80 cloud flashes. For ground flash, the LIS recorded the subsequent strokes and changes inside the cloud. For cloud flashes, LIS recorded those with higher sources in altitude and larger number of sources. The discrepancies between the LIS and LDAR flash locations are about 4.3 km for cloud flashes and 12.2 km for ground flashes. The reason for these differences remain a mystery.

Description: Since April 1995, lightning activity around the globe has been monitored with the Optical Transient Detector (OTD). The OTD observations acquired during the one year period from September 1995 through August 1996 have been used to statistically determine the number of flashes that occur over the Earth during each hour of the diurnal cycle, expressed both as a function of local time and universal time. The globally averaged local [il,htnina activity displays a peak in late afternoon (1500-1800 local time) and a minimum in the morning hours (0600- 1000 local time) consistent with convection associated with diurnal heating. No diurnal variation is found for oceanic storms. The diurnal lightning distribution (universal time) for the globe displays a variation of about 35% about its mean as compared to the Carnegie curve which has a variation of only 15% above and below the mean.

Description: Many state and local air quality agencies use the U.S. Environmental Protection Agency (EPA) Community Multiscale Air Quality (CMAQ) modeling system to determine compliance with the National Ambient Air Quality Standards (NAAQS). Because emission reduction scenarios are tested using CMAQ with an aim of determining the most efficient and cost effective strategies for attaining the NAAQS, it is very important that trace gas concentrations derived by CMAQ are accurate. Overestimating concentrations can literally translate into billions of dollars lost by commercial and government industries forced to comply with the standards. Costly health, environmental and socioeconomic problems can result from concentration underestimates. Unfortunately, lightning modeling for CMAQ is highly oversimplified. This leads to very poor estimates of lightning-produced nitrogen oxides "NOx" (= NO + NO2) which directly reduces the accuracy of the concentrations of important CMAQ trace gases linked to NOx concentrations such as ozone and methane. Today it is known that lightning is the most important NOx source in the upper troposphere with a global production rate estimated to vary between 2-20 Tg(N)/yr. In addition, NOx indirectly influences our climate since it controls the concentration of ozone and hydroxyl radicals (OH) in the atmosphere. Ozone is an important greenhouse gas and OH controls the oxidation of various greenhouse gases. We describe a robust NASA lightning model, called the Lightning Nitrogen Oxides Model (LNOM) that combines state-of-the-art lightning measurements, empirical results from field studies, and beneficial laboratory results to arrive at a realistic representation of lightning NOx production for CMAQ. NASA satellite lightning data is used in conjunction with ground-based lightning detection systems to assure that the best representation of lightning frequency, geographic location, channel length, channel altitude, strength (i.e., channel peak current), and number of strokes per flash are accounted for. LNOM combines all of these factors in a straightforward approach that is easily implemented into CMAQ. We anticipate that future applications of LNOM will produce significant and important changes in CMAQ trace gas concentrations for various regions and times. We also anticipate that these changes will have a direct impact on decision makers responsible for NAAQS attainment.

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 linear algebraic solution is provided for the problem of retrieving the location and time of occurrence of lightning ground strikes from an Advanced Lightning Direction Finder (ALDF) network. The ALDF network measures field strength, magnetic bearing and arrival time of lightning radio emissions. Solutions for the plane (i.e., no Earth curvature) are provided that implement all of tile measurements mentioned above. Tests of the retrieval method are provided using computer-simulated data sets. We also introduce a quadratic planar solution that is useful when only three arrival time measurements are available. The algebra of the quadratic root results are examined in detail to clarify what portions of the analysis region lead to fundamental ambiguities in source location. Complex root results are shown to be associated with the presence of measurement errors when the lightning source lies near an outer sensor baseline of the ALDF network. In the absence of measurement errors, quadratic root degeneracy (no source location ambiguity) is shown to exist exactly on the outer sensor baselines for arbitrary non-collinear network geometries. The accuracy of the quadratic planar method is tested with computer generated data sets. The results are generally better than those obtained from the three station linear planar method when bearing errors are about 2 deg. We also note some of the advantages and disadvantages of these methods over the nonlinear method of chi(sup 2) minimization employed by the National Lightning Detection Network (NLDN) and discussed in Cummins et al.(1993, 1995, 1998).

Description: A "dimensional reduction" (DR) method is introduced for analyzing lightning field changes whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight to just four. The four unknowns are found by performing a numerical minimization of a chi-squared goodness-of-fit function. At each step of the minimization, an Overdetermined Fixed Matrix (OFM) method is used to immediately retrieve the best "residual source". In this way, all 8 parameters are found, yet a numerical search of only 4 parameters is required. The inversion method is applied to the understanding of lightning charge retrievals. The accuracy of the DR method has been assessed by comparing retrievals with data provided by the Lightning Detection And Ranging (LDAR) instrument. Because lightning effectively deposits charge within thundercloud charge centers and because LDAR traces the geometrical development of the lightning channel with high precision, the LDAR data provides an ideal constraint for finding the best model charge solutions. In particular, LDAR data can be used to help determine both the horizontal and vertical positions of the model charges, thereby eliminating dipole ambiguities. The results of the LDAR-constrained charge retrieval method have been compared to the locations of optical pulses/flash locations detected by the Lightning Imaging Sensor (LIS).

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.