William J. Koshak

Global frequency and distribution of lightning as observed from space by the Optical Transient Detector

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. The Congo basin, which stands out year-round, shows a peak mean annual flash density of 80 fl km 2 yr 1 in Rwanda, and includes an area of over 3 million km 2 exhibiting flash densities greater than 30 fl km 2 yr 1 (the flash density of central Florida). Lightning is predominant in the northern Atlantic and western Pacific Ocean basins year-round where instability is produced from cold air passing over warm ocean water. Lightning is less frequent in the eastern tropical Pacific and Indian Ocean basins where the air mass is warmer. A dominant Northern Hemisphere summer peak occurs in the annual cycle, and evidence is found for a tropically driven semiannual cycle. INDEX TERMS: 3304 Meteorology and Atmospheric Dynamics: Atmospheric electricity; 3309 Meteorology and Atmospheric Dynamics: Climatology (1620); 3324 Meteorology and Atmospheric Dynamics: Lightning; 3394 Meteorology and Atmospheric Dynamics: Instruments and techniques;

Performance Assessment of the Optical Transient Detector and Lightning Imaging Sensor. Part I: Predicted Diurnal Variability

Abstract Laboratory calibration and observed background radiance data are used to determine the effective sensitivities of the Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS), 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 ± 0.7 and 7.6 ± 3.3 μJ sr−1 m−2 for night and local noon; the OTD thresholds are 11.7 ± 2.2 and 16.8 ± 4.6 μJ sr−1 m−2. LIS and OTD minimum signal-to-noise ratios occur from 0800 to 1600 local time, and attain values of 10 ± 2 and 20 ± 3, respectively. False alarm rate due to instrument noise yields ∼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 ± 4% and 73 ± 11% for LIS night and noon; 56 ± 7% and 44 ± 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 det...

The Optical Transient Detector (OTD): Instrument Characteristics and Cross-Sensor Validation

Abstract Lightning data from the U.S. National Lightning Detection Network (NLDN) are used to perform preliminary validation of the satellite-based Optical Transient Detector (OTD). Sensor precision, accuracy, detection efficiency, and biases of the deployed instrument are considered. The sensor is estimated to have, on average, about 20–40-km spatial and better than 100-ms temporal accuracy. The detection efficiency for cloud-to-ground lightning is about 46%–69%. It is most likely slightly higher for intracloud lightning. There are only marginal day/night biases in the dataset, although 55- or 110-day averaging is required to remove the sampling-based diurnal lightning cycle bias.

Laboratory Calibration of the Optical Transient Detector and the Lightning Imaging Sensor

Abstract The authors present in detail the laboratory apparatus and techniques that were used to complete a full radiometric calibration of two space-based lightning detectors: the optical transient detector (OTD) and the lightning imaging sensor (LIS) that were developed at the National Aeronautics and Space Administration Marshall Space Flight Center. These instruments are nadir-staring imagers that are optimized to detect and locate lightning from low-Earth orbit during day and night conditions. The radiometric calibration consisted of characterizing the pixel response to steady and transient optical sources, sensor field of view, and sensor spectral response. The transient optical signals produced in the calibration laboratory were used to derive estimates of sensor lightning detection efficiency.

Diffusion model for lightning radiative transfer

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.

Variability of CONUS Lightning in 2003–12 and Associated Impacts

AbstractChanges in lightning characteristics over the conterminous United States (CONUS) are examined to support the National Climate Assessment (NCA) program. Details of the variability of cloud-to-ground (CG) lightning characteristics over the decade 2003–12 are provided using data from the National Lightning Detection Network (NLDN). Changes in total (CG + cloud flash) lightning across part of the CONUS during the decade are provided using satellite Lightning Imaging Sensor (LIS) data. The variations in NLDN-derived CG lightning are compared with available statistics on lightning-caused impacts to various U.S. economic sectors. Overall, a downward trend in total CG lightning count is found for the decadal period; the 5-yr mean NLDN CG count decreased by 12.8% from 25 204 345.8 (2003–07) to 21 986 578.8 (2008–12). There is a slow upward trend in the fraction and number of positive-polarity CG lightning, however. Associated lightning-caused fatalities and injuries, and the number of lightning-caused wild...

On the retrieval of lightning radio sources from time-of-arrival data

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.

General Matrix Inversion Technique for the Calibration of Electric Field Sensor Arrays on Aircraft Platforms

Abstract A matrix calibration procedure has been developed that uniquely relates the electric fields measured at the aircraft with the external vector electric field and net aircraft charge. The calibration method can be generalized to any reasonable combination of electric field measurements and aircraft. A calibration matrix is determined for each aircraft that represents the individual instrument responses to the external electric field. The aircraft geometry and configuration of field mills (FMs) uniquely define the matrix. The matrix can then be inverted to determine the external electric field and net aircraft charge from the FM outputs. A distinct advantage of the method is that if one or more FMs need to be eliminated or deemphasized (e.g., due to a malfunction), it is a simple matter to reinvert the matrix without the malfunctioning FMs. To demonstrate the calibration technique, data are presented from several aircraft programs (ER-2, DC-8, Altus, and Citation).

A Linear Method for Analyzing Lightning Field Changes

Abstract A constrained, least-squares method for analyzing multiple-station measurements of lightning field changes (ΔEs) is introduced. Previous methods have attempted to fit the spatial pattern of lightning ΔEs using nonlinear models, such as a point charge (Q) or a point dipole (P) model. With the linear method, the ΔEs are described not by models but by a general volume charge distribution that is deposited on a large (40 × 40 × 20 km3) Cartesian grid above the measuring network. A linear system of equations is used to relate the measured ΔEs 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 liner 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 steepe...

Time-averaged current analysis of a thunderstorm using ground-based measurements

The amount of upward current provided to the ionosphere by a thunderstorm that appeared over the Kennedy Space Center (KSC) on July 11, 1978, is reexamined using an analytic equation that describes a bipolar thunderstorms current contribution to the global circuit in terms of its generator current, lightning currents, the altitudes of its charge centers, and the conductivity profile of the atmosphere. Ground-based measurements, which were obtained from a network of electric field mills positioned at various distances from the thunderstorm, were used to characterize the electrical activity inside the thundercloud. The location of the lightning discharges, the type of lightning, and the amount of charge neutralized during this thunderstorm were computed through a least squares inversion of the measured changes in the electric fields following each lightning discharge. These measurements provided the information necessary to implement the analytic equation, and consequently, a time-averaged estimate of this thunderstorms current contribution to the global circuit was calculated. From these results the amount of conduction current supplied to the ionosphere by this small thunderstorm was computed to be less than 25% of the time-averaged generator current that flowed between the two vertically displaced charge centers.