ALBERT

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: Electric field measurements are fundamental to the study of thunderstorm electrification, thundercloud charge structure, and the determination of the locations and magnitudes of charges deposited by lightning. Continuous field observations can also be used to warn of impending electrical hazards. For example, the USAF Eastern Range (ER) and NASA Kennedy Space Center (KSC) in Florida currently operate a ground-based network of electric field mill sensors to warn against lightning hazards to space vehicle operations/launches. The sensors provide continuous recordings of the ambient field. Others investigators have employed flat-plate electric field antennas to detect changes In the ambient field due to lightning. In each approach, electronic circuitry is used to directly detect and amplify the effects of the ambient field on an exposed metal conductor (antenna plate); in the case of continuous field recordings, the antenna plate is alternately shielded and unshielded by a grounded conductor. In this work effort, an alternate optical method for detecting lightning-caused electric field changes is Introduced. The primary component in the detector is an anisotropic electro-optic crystal of potassium di-hydrogen phosphate (chemically written as KH2PO4 (KDP)). When a voltage Is placed across the electro-optic crystal, the refractive Indices of the crystal change. This change alters the polarization state of a laser light beam that is passed down the crystal optic axis. With suitable application of vertical and horizontal polarizers, a light transmission measurement is related to the applied crystal voltage (which in turn Is related to the lightning caused electric field change). During the past two years, all critical optical components were procured, assembled, and aligned. An optical housing, calibration set-up, and data acquisition system was integrated for breadboard testing. The sensor was deployed at NASA Marshall Space Flight Center (MSFC) in the summer of 1998 to collect storm data. Because solid-state technology is used, future designs of the sensor will be significantly scaled down In physical dimension and weight compared to the present optical breadboard prototype. The use of fiber optics would also provide significant practical improvements.

Description: Changes in the surface electric field are frequently used to infer the locations and magnitudes of lightning-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q-model) or a point dipole (the P-model). The Q-model has 4 unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P-model has 6 unknown parameters and describes many intracloud (IC) discharges. In this paper, we introduce a new analysis method that assumes that the change in the cloud charge can be described by a truncated multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. If there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a 3-dimensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been tested on computer simulated sources and on natural lightning at the NASA Kennedy Space Center and USAF Eastern Range.

Description: A two-space scatterer formalism and equivalent medium approach of Twersky are used to obtain formulae for the bulk electromagnetic parameters of a thundercloud medium that is illuminated by lightning optical emissions. A modified WKB approximation is applied to derive the two-space scattering amplitude. Optical constants of dry air, moist atmosphere, and water,.are inserted into the formulae to generate numerical values via iteration. The two-space scatterer formalism results are close to those obtained from free- or sin-le-space formalisms for the dilute case. The numerical values of the bulk parameters are required to successfully transform the scattering problem to that of an equivalent obstacle excited by an incident wave traveling in K - space but radiating in k(sub 1) -space.