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NASA NTRS2004

Software Assurance of PLCs Training Course

Being heavily visually-oriented, I am a firm believer in communication and conveying emotions through the art of color, motion, and transformation. A four-part online training course was created in PowerPoint and needed to be translated over into a Flash format. Issues with the Powerpoint were that the size of the files caused noticeable delays when placed online, there were compatibility issues, and from a composition and design perspective, color schemes and layout left much to be desired. High contrast, pixilated yellow text spiraling and flying on to a background of overly rich hues of blue with cheesy gradient patterns was just not appeasing to my eye, along with the menu directory buttons located at the top resembling blue pills of NyQuil on top of a stale gray border that had nothing to do with the background. The course itself is extremely broad and verbose, and will get monotonous very soon after starting. Moving about the course was very cumbersome as well. efficient by drastically reducing the size (The file size of all four parts of the actual course combined will ultimately not even be a fifth as big as one part of the original PowerPoint alone!); along with that, the course was made to be more interactive and user-friendly, as well as pleasing to the eye. Upon being viewed by fellow co-workers, nothing but positive feedback has been received. When beginning the presentation, onscreen comes a 3' 2" chubby, balding professor, who is a master in his knowledge of Programmable Logic Controllers (PLCs). He introduces himself and presents all of his vast knowledge over PLCs in a fun and innovative manner, making it much easier to acquire the information presented. A Scene Selection feature has been added making it a lot easier to jump from part to part and the back and forth arrows are much easier to utilize, and they are both less obtrusive than its PowerPoint predecessor. The user can also go at their pace, as the presentation pauses after at the end of each statement. computer animation, it was.. .still. ..animation done on a computer. I was able to incorporate my artistic talent and intuitive creativity into it, one thing I am very proficient at doing when it comes to what I do and what I will do in my profession as an artist/computer animator. At first, I felt that there was no place for an artist within a faculty of scientists, engineers, chemists, mathematicians, and programmers, but I managed to fit in quite successfully. My task was to convert the course into a Flash format, which would make it much more My project surprisingly somewhat dealt with my field of interest-though it was not

Threatt, Jamarr↗
NASA NTRS2006

A Probable Taurid Impact on the Moon

On November 7, 2005, at 23:41:52 UT, observers located at the Marshall Space Flight Center captured the flash produced by a kilogram-size meteoroid striking the lunar surface. Photometric analysis of the event video, combined with the plausible assumptions of a luminous efficiency of 2x10" and that the meteoroid was a member of the Taurid meteoroid stream, yield a striking power of approximately 640 lbs of TNT and a mass of approximately 3.8 kg. Even though no confirming independent observations are known to exist, there is high confidence in the impact origin of the flash; reasonable attempts have been made to eliminate other possibilities, such as cosmic ray hits on the CCD and glints from satellites that may have crossed the lunar disk near the impact time.

Cooke, William J.↗
NASA NTRS2006

Single Event Effects Test Results for the Actel ProASIC Plus and Altera Stratix-II Field Programmable Gate Arrays

This work describes radiation testing of Actel's ProASIC Plus and Altera's Stratix-II FPGAs. The Actel Device Under Test (DUT) was a ProASIC Plus APA300-PQ208 nonvolatile, field reprogrammable device which is based on a 0.22micron flash-based LVCMOS technology. Limited investigation has taken place into flash based FPGA technologies, therefore this test served as a preliminary reference point for various SEE behaviors. The Altera DUT was a Stratix-II EP2S60F1020C4. Single Event Upset (SEU) and Single Event Latchup (SEL) were the focus of these studies. For the Actel, a latchup test was done at an effective LET of 75.0 MeV-sq cm/mg at room temperature, and no latchup was detected when irradiated to a total fluence of 1 x 10(exp 7) particles/sq cm. The Altera part was shown to latchup at room temperature.

heavy ions↗
NASA NTRS2007

GCR-induced Photon Luminescence of the Moon: The Moon as a CR Detector

We report on the results of a preliminary study of the GCR-induced photon luminescence of the Moon using the Monte Carlo program FLUKA. The model of the lunar surface is taken to be the chemical composition of soils found at various landing sites during the Apollo and Luna programs, averaged over all such sites to define a generic regolith for the present analysis. This then becomes the target that is bombarded by Galactic Cosmic Rays (GCRs) in FLUKA to determine the photon fluence when there is no sunshine or Earthshine. From the photon fluence we derive the energy spectrum which can be utilized to design an orbiting optical instrument for measuring the GCR-induced luminescence. This is to be distinguished from the gamma-ray spectrum produced by the radioactive decay of its radiogenic constituents lying in the surface and interior. Also, we investigate transient optical flashes from high-energy CRs impacting the lunar surface (boulders and regolith). The goal is to determine to what extent the Moon could be used as a rudimentary CR detector. Meteor impacts on the Moon have been observed for centuries to generate such flashes, so why not CRs?

Wilson, Thomas L.↗
NASA NTRS2007

Diurnal Lightning Distributions as Observed by the Optical Transient Detector (OTD) and the Lightning Imaging Sensor (LIS)

Data obtained from the OTD (April 1995 to March 2000) and LIS (December 1997 to December 2005) satellites (70 and 35 degree inclination low earth orbits, respectively) are used to statistically determine the number of flashes in the diurnal cycle both as a function of local and universal time. Also included are global flash density maps. The data is further subdivided by season, continental versus oceanic, night time versus day time, northern versus southern hemisphere, and other regions of interest such as the Brazilian rain forest and the Congo. The data includes corrections for detection efficiency and instrument view time. The data was compared with the "Carnegie Curve" and the diurnal global thunderstorm contributions from thunderday statistics fiom different continents as derived by Whipple and Scrase, 1936. Initial results indicate that the northern hemisphere fall (September to November) has a larger amplitude than the northern hemisphere spring (March to May). This may be due to the differences in the contribution of the Brazilian rain forest during these periods (the main lightning peak starts in September and ends in February with a secondary peak in April). For some areas of the world, the peak of the diurnal curve appears to be shifted to later in the evening.

Blakeslee, R. J.↗
NASA NTRS2004

Satellite Observations of Spatial and Interannual Variability of Lightning and Radar Reflectivity

The authors use satellite data to examine the relationship between lightning and upper-level radar reflectivity. They find correlations between average flash rates and upper-level reflectivities over both land and ocean, although both flash rates and reflectivities are much lower over ocean than land. Analysis of the data using Empirical Orthogonal Functions (EOFs) shows similar EOFs for averaged lightning and reflectivity. In contrast, the EOFs of the anomalies of lightning and reflectivity have different spatial patterns; however, both have principal component time series that are correlated with the Southern Oscillation Index and, hence, El Nino. Differences in behavior of the lightning and reflectivity anomaly EOFs and principal components suggest that El Nino plays a smaller role in lightning anomaly than precipitation anomaly.

lightning↗
NASA NTRS2007

Diurnal Lightning Distributions as Observed by the Optical Transient Detector (OTD) and the Lightning Imaging Sensor (LIS)

Data obtained from the OTD (April 1995 to March 2000) and LIS (December 1997 to December 2005) satellites (70 and 35 degree inclination low earth orbits, respectively) are used to statistically determine the number of flashes in the diurnal cycle both as a function of local and universal time. Also included are global flash density maps. The data are further subdivided by season, continental versus oceanic, night time versus day time, northern versus southern hemisphere, and other regions of interest. The data include corrections for detection efficiency and instrument view time. The data are compared with both the "Carnegie Curve" and the diurnal global thunderstorm contributions from thunderday statistics from different continents, and are found to agree closely in phase and amplitude with the global thunderday statistics. The analysis also indicates that the southern hemisphere spring (September to November) has larger amplitude than the southern hemisphere fall (March to May). This may be due to differences in the contribution from the Brazilian rain forest during these periods. In general, as highlighted by a difference analysis, more lightning is observed in local springtime than the fall for continental locations, while oceanic regions display an opposite effect. For some areas of the world, the peak of diurnal curve appears to be shifted to later in the evening.

Bailey, Jeff C.↗
NASA NTRS2007

Electric Field and Lightning Observations in the Core of Category 5 Hurricane Emily

Significant electric fields and lightning activity associated with Hurricane Emily were observed from a NASA high-altitude ER-2 aircraft on July 17, 2005 while this storm developed as a compact but intense category 5 hurricane in the Caribbean south of Cuba. The electrical measurements were acquired as part of the NASA sponsored Tropical Cloud Systems and Processes (TCSP) experiment. In addition to the electrical measurements, the aircraft's remote sensing instrument complement also included active radars, passive microwave, visible and infrared radiometers, and a temperature sounder providing details on the dynamical, microphysical, and environmental structure, characteristics and development of this intense storm. Cloud-to-ground lightning location data from Vaisala's long range lightning detection network were also acquired and displayed in real-time along with electric fields measured at the aircraft. These data and associated display also supported aircraft guidance and vectoring during the mission. During the observing period, flash rates in excess of 3 to 5 flashes per minute, as well as large electric field and field change values were observed as the storm appeared to undergo periods of intensification, especially in the northwest quadrant in the core eyewall regions. This is in contrast to most hurricanes that tend to be characterized by weak electrification and little or no lightning activity except in the outer rain bands. It should be noted that this storm also had significant lightning associated with its rain bands.

Blakeslee, Richard↗
NASA NTRS2007

Response of Global Lightning Activity Observed by the TRMM/LIS During Warm and Cold ENSO Phases

This paper investigates the response of global lightning activity to the transition from the warm (January February March-JFM 1998) to the cold (JFM 1999) ENSO phase. The nine-year global lightning climatology for these months from the Tropical Rainfall Measuring Mission (TRMM) Lightning Imaging Sensor (LIS) provides the observational baseline. Flash rate density is computed on a 5.0x5.0 degree lat/lon grid within the LIS coverage area (between approx.37.5 N and S) for each three month period. The flash rate density anomalies from this climatology are examined for these months in 1998 and 1999. The observed lightning anomalies spatially match the documented general circulation features that accompany the warm and cold ENSO events. During the warm ENSO phase the dominant positive lightning anomalies are located mostly over the Western Hemisphere and more specifically over Gulf of Mexico, Caribbean and Northern Mid-Atlantic. We further investigate specifically the Northern Mid-Atlantic related anomaly features since these show strong relation to the North Atlantic Oscillation (NAO). Furthermore these observed anomaly patterns show strong spatial agreement with anomalous upper level (200 mb) cold core cyclonic circulations. Positive sea surface temperature anomalies during the warm ENSO phase also affect the lightning activity, but this is mostly observed near coastal environments. Over the open tropical oceans, there is climatologically less lightning and the anomalies are less pronounced. Warm ENSO related anomalies over the Eastern Hemisphere are most prominent over the South China coast. The transition to the cold ENSO phase illustrates the detected lightning anomalies to be more pronounced over East and West Pacific. A comparison of total global lightning between warm and cold ENSO phase reveals no significant difference, although prominent regional anomalies are located over mostly oceanic environments. All three tropical "chimneys" (Maritime Continent, Central Africa, and Amazon Basin) do not show any particular response to this transition.

Chronis, Themis G.↗
NASA NTRS2008

Determination of a Limited Scope Network's Lightning Detection Efficiency

This paper outlines a modeling technique to map lightning detection efficiency variations over a region surveyed by a sparse array of ground based detectors. A reliable flash peak current distribution (PCD) for the region serves as the technique's base. This distribution is recast as an event probability distribution function. The technique then uses the PCD together with information regarding: site signal detection thresholds, type of solution algorithm used, and range attenuation; to formulate the probability that a flash at a specified location will yield a solution. Applying this technique to the full region produces detection efficiency contour maps specific to the parameters employed. These contours facilitate a comparative analysis of each parameter's effect on the network's detection efficiency. In an alternate application, this modeling technique gives an estimate of the number, strength, and distribution of events going undetected. This approach leads to a variety of event density contour maps. This application is also illustrated. The technique's base PCD can be empirical or analytical. A process for formulating an empirical PCD specific to the region and network being studied is presented. A new method for producing an analytical representation of the empirical PCD is also introduced.

Rompala, John T.↗
NASA NTRS2006

Preliminary Trade Study of Phase Change Heat Sinks

For short durations, phase change based heat rejection systems are a very effective way of removing heat from spacecraft. Future NASA vehicles, such as the Crew Exploration Vehicle (CEV), will require non-radiative heat rejection systems during at least a portion of the planned mission, just as their predecessors have. While existing technologies are available to modify, such as Apollo era sublimators, or the Space Shuttle Flash Evaporator System (FES), several new technologies are under development or investigation to progress beyond these existing heat rejection systems. Examples include the Multi-Fluid Evaporator developed by Hamilton Sundstrand, improvements upon the Contaminant Insensitive Sublimator originally developed for the X-38 program, and a Compact Flash Evaporator System (CFES). Other possibilities evaluate new ways of operating existing designs. The new developments are targeted at increasing operating life, expanding the environments in which the system can operate, improving the mass and volume characteristics, or some combination of these or other improvements. This paper captures the process and results of a preliminary trade study performed at Johnson Space Center to compare the various existing and proposed phase change based heat rejection systems for the CEV. Because the new systems are still in development, and the information on existing systems is extrapolation, this trade study is not meant to suggest a final decision for future vehicles. The results of this early trade study are targeted to aid the development efforts for the new technologies by identifying issues that could reduce the chances of selection for the CEV.

Anderson, Molly↗
NASA NTRS2008

Light Echos in Kerr Geometry: A Source of High Frequency QPOs from Random X-ray Bursts

We propose that high frequency quasi-periodic oscillations (HFQPOs) can be produced from randomly-formed X-ray bursts (flashes) by plasma interior to the ergosphere of a rapidly-rotating black hole. We show by direct computation of their orbits that the photons comprising the observed X-ray light curves, if due to a multitude of such flashes, are affected significantly by the black hole's dragging of inertial frames; the photons of each such burst arrive to an observer at infinity in multiple (double or triple), distinct 'bunches' separated by a roughly constant time lag of t/M approximately equal to 14, regardless of the bursts' azimuthal position. We argue that every other such 'bunch' represents photons that follow trajectories with an additional orbit around the black hole at the photon circular orbit radius (a photon 'echo'). The presence of this constant lag in the response function of the system leads to a QPO feature in its power density spectra, even though the corresponding light curve consists of a totally stochastic signal. This effect is by and large due to the black hole spin and is shown to gradually diminish as the spin parameter a decreases or the radial position of the burst moves outside the static limit surface (ergosphere). Our calculations indicate that for a black hole with Kerr parameter of a/M=0.99 and mass of M=10*Msun the QPO is expected at a frequency of approximately 1.3-1.4 kHz. We discuss the plausibility and observational implications of our model/results as well as its limitations.

Fukumura, K.↗
NASA NTRS2008

Light Echoes in Kerr Geometry: A Source of High Frequency QPOs from Random X-ray Bursts

We propose that high frequency quasi-periodic oscillations (HFQPOs) can be produced from randomly-formed X-ray bursts (flashes) by plasma interior to the ergosphere of a rapidly-rotating black hole. We show by direct computation of their orbits that the photons comprising the observed X-ray light curves, if due to a multitude of such flashes, are affected significantly by the black hole's dragging of inertial frames; the photons of each such burst arrive to an observer at infinity in multiple (double or triple), distinct "bunches" separated by a roughly constant time lag of Deltat(t(sub lag))/M approx. 14, regardless of the bursts' azimuthal position. We argue that every other such "bunch" represents photons that follow trajectories with an additional orbit around the black hole at the photon circular orbit radius (a photon "echo"). The presence of this constant lag in the response function of the system leads to a QPO feature in its power density spectra, even though the corresponding light curve consists of a totally stochastic signal. This effect is by and large due to the black hole spin and is shown to gradually diminish as the spin parameter a decreases or the radial position of the burst moves outside the static limit surface (ergosphere). Our calculations indicate that for a black hole with Kerr parameter of a/M = 0.99 and mass of M = 10Stellar Mass the QPO is expected at a frequency of v(sub QPO) approx. 1.3 - 1.4 kHz. We discuss the plausibility and observational implications of our model/results as well as its limitations. Subject headings: accretion, accretion disks - black hole physics - X-rays: galaxies - stars: oscillations

Fukumura, Keigo↗
NASA NTRS2006

Single Event Effects Test Results for Advanced Field Programmable Gate Arrays

Reconfigurable Field Programmable Gate Arrays (FPGAs) from Altera and Actel and an FPGA-based quick-turnApplication Specific Integrated Circuit (ASIC) from Altera were subjected to single-event testing using heavy ions. Both Altera devices (Stratix II and HardCopy II) exhibited a low latchup threshold (below an LET of 3 MeV-cm2/mg) and thus are not recommended for applications in the space radiation environment. The flash-based Actel ProASIC Plus device did not exhibit latchup to an effective LET of 75 MeV-cm2/mg at room temperature. In addition, these tests did not show flash cell charge loss (upset) or retention damage. Upset characterization of the design-level flip-flops yielded an LET threshold below 10 MeV-cm2/mg and a high LET cross section of about lxlO-6 cm2/bit for storing ones and about lxl0-7 cm2/bit for storing zeros . Thus, the ProASIC device may be suitable for critical flight applications with appropriate triple modular redundancy mitigation techniques.

Field Programmable Gate Arrays↗
NASA NTRS2009

Satellite Proving Ground for the GOES-R Geostationary Lightning Mapper (GLM)

The key mission of the Satellite Proving Ground is to demonstrate new satellite observing data, products and capabilities in the operational environment to be ready on Day 1 to use the GOES-R suite of measurements. Algorithms, tools, and techniques must be tested, validated, and assessed by end users for their utility before they are finalized and incorporated into forecast operations. The GOES-R Proving Ground for the Geostationary Lightning Mapper (GLM) focuses on evaluating how the infusion of the new technology, algorithms, decision aids, or tailored products integrate with other available tools (weather radar and ground strike networks; nowcasting systems, mesoscale analysis, and numerical weather prediction models) in the hands of the forecaster responsible for issuing forecasts and warning products. Additionally, the testing concept fosters operation and development staff interactions which will improve training materials and support documentation development. Real-time proxy total lightning data from regional VHF lightning mapping arrays (LMA) in Northern Alabama, Central Oklahoma, Cape Canaveral Florida, and the Washington, DC Greater Metropolitan Area are the cornerstone for the GLM Proving Ground. The proxy data will simulate the 8 km Event, Group and Flash data that will be generated by GLM. Tailored products such as total flash density at 1-2 minute intervals will be provided for display in AWIPS-2 to select NWS forecast offices and national centers such as the Storm Prediction Center. Additional temporal / spatial combinations are being investigated in coordination with operational needs and case-study proxy data and prototype visualizations may also be generated from the NASA heritage Lightning Imaging Sensor and Optical Transient Detector data. End users will provide feedback on the utility of products in their operational environment, identify use cases and spatial/temporal scales of interest, and provide feedback to the developers for adjusted or new products.

Goodman, Steven J.↗
NASA NTRS2009

OP09O-OP404-9 Wide Field Camera 3 CCD Quantum Efficiency Hysteresis

The HST/Wide Field Camera (WFC) 3 UV/visible channel CCD detectors have exhibited an unanticipated quantum efficiency hysteresis (QEH) behavior. At the nominal operating temperature of -83C, the QEH feature contrast was typically 0.1-0.2% or less. The behavior was replicated using flight spare detectors. A visible light flat-field (540nm) with a several times full-well signal level can pin the detectors at both optical (600nm) and near-UV (230nm) wavelengths, suppressing the QEH behavior. We are characterizing the timescale for the detectors to become unpinned and developing a protocol for flashing the WFC3 CCDs with the instrument's internal calibration system in flight. The HST/Wide Field Camera 3 UV/visible channel CCD detectors have exhibited an unanticipated quantum efficiency hysteresis (QEH) behavior. The first observed manifestation of QEH was the presence in a small percentage of flat-field images of a bowtie-shaped contrast that spanned the width of each chip. At the nominal operating temperature of -83C, the contrast observed for this feature was typically 0.1-0.2% or less, though at warmer temperatures contrasts up to 5% (at -50C) have been observed. The bowtie morphology was replicated using flight spare detectors in tests at the GSFC Detector Characterization Laboratory by power cycling the detector while cold. Continued investigation revealed that a clearly-related global QE suppression at the approximately 5% level can be produced by cooling the detector in the dark; subsequent flat-field exposures at a constant illumination show asymptotically increasing response. This QE "pinning" can be achieved with a single high signal flat-field or a series of lower signal flats; a visible light (500-580nm) flat-field with a signal level of several hundred thousand electrons per pixel is sufficient for QE pinning at both optical (600nm) and near-UV (230nm) wavelengths. We are characterizing the timescale for the detectors to become unpinned and developing a protocol for flashing the WFC3 CCDs with the instrument's internal calibration system in flight. A preliminary estimate of the decay timescale for one detector is that a drop of 0.1-0.2% occurs over a ten day period, indicating that relatively infrequent cal lamp exposures can mitigate the behavior to extremely low levels.

Collins, Nick↗
NASA NTRS2007

Analog Nonvolatile Computer Memory Circuits

In nonvolatile random-access memory (RAM) circuits of a proposed type, digital data would be stored in analog form in ferroelectric field-effect transistors (FFETs). This type of memory circuit would offer advantages over prior volatile and nonvolatile types: In a conventional complementary metal oxide/semiconductor static RAM, six transistors must be used to store one bit, and storage is volatile in that data are lost when power is turned off. In a conventional dynamic RAM, three transistors must be used to store one bit, and the stored bit must be refreshed every few milliseconds. In contrast, in a RAM according to the proposal, data would be retained when power was turned off, each memory cell would contain only two FFETs, and the cell could store multiple bits (the exact number of bits depending on the specific design). Conventional flash memory circuits afford nonvolatile storage, but they operate at reading and writing times of the order of thousands of conventional computer memory reading and writing times and, hence, are suitable for use only as off-line storage devices. In addition, flash memories cease to function after limited numbers of writing cycles. The proposed memory circuits would not be subject to either of these limitations. Prior developmental nonvolatile ferroelectric memories are limited to one bit per cell, whereas, as stated above, the proposed memories would not be so limited. The design of a memory circuit according to the proposal must reflect the fact that FFET storage is only partly nonvolatile, in that the signal stored in an FFET decays gradually over time. (Retention times of some advanced FFETs exceed ten years.) Instead of storing a single bit of data as either a positively or negatively saturated state in a ferroelectric device, each memory cell according to the proposal would store two values. The two FFETs in each cell would be denoted the storage FFET and the control FFET. The storage FFET would store an analog signal value, between the positive and negative FFET saturation values. This signal value would represent a numerical value of interest corresponding to multiple bits: for example, if the memory circuit were designed to distinguish among 16 different analog values, then each cell could store 4 bits. Simultaneously with writing the signal value in the storage FFET, a negative saturation signal value would be stored in the control FFET. The decay of this control-FFET signal from the saturation value would serve as a model of the decay, for use in regenerating the numerical value of interest from its decaying analog signal value. The memory circuit would include addressing, reading, and writing circuitry that would have features in common with the corresponding parts of other memory circuits, but would also have several distinctive features. The writing circuitry would include a digital-to-analog converter (DAC); the reading circuitry would include an analog-to-digital converter (ADC). For writing a numerical value of interest in a given cell, that cell would be addressed, the saturation value would be written in the control FFET in that cell, and the non-saturation analog value representing the numerical value of interest would be generated by use of the DAC and stored in the storage FFET in that cell. For reading the numerical value of interest stored in a given cell, the cell would be addressed, the ADC would convert the decaying control and storage analog signal values to digital values, and an associated fast digital processing circuit would regenerate the numerical value from digital values.

MacLeod, Todd↗
NASA NTRS2009

Global Electric Circuit Implications of Total Current Measurements over Electrified Clouds

We determined total conduction (Wilson) currents and flash rates for 850 overflights of electrified clouds spanning regions including the Southeastern United States, the Western Atlantic Ocean, the Gulf of Mexico, Central America and adjacent oceans, Central Brazil, and the South Pacific. The overflights include storms over land and ocean, with and without lightning, and with positive and negative Wilson currents. We combined these individual storm overflight statistics with global diurnal lightning variation data from the Lightning Imaging Sensor (LIS) and Optical Transient Detector (OTD) to estimate the thunderstorm and electrified shower cloud contributions to the diurnal variation in the global electric circuit. The contributions to the global electric circuit from lightning producing clouds are estimated by taking the mean current per flash derived from the overflight data for land and ocean overflights and combining it with the global lightning rates (for land and ocean) and their diurnal variation derived from the LIS/OTD data. We estimate the contribution of non-lightning producing electrified clouds by assuming several different diurnal variations and total non-electrified storm counts to produce estimates of the total storm currents (lightning and non-lightning producing storms). The storm counts and diurnal variations are constrained so that the resultant total current diurnal variation equals the diurnal variation in the fair weather electric field (+/-15%). These assumptions, combined with the airborne and satellite data, suggest that the total mean current in the global electric circuit ranges from 2.0 to 2.7 kA, which is greater than estimates made by others using other methods.

Mach, Douglas M.↗