[1] The Los Alamos Sferic Array (LASA) recorded VLF/LF electric-field-change signals from over ten million lightning discharges during the period from 1998 to 2001. Using the differential-times-of-arrival of lightning sferics recorded by three or more stations, the latitudes and longitudes of the source discharges were determined. Under conditions of favorable geometry and ionospheric propagation, sensors obtained ionospherically reflected skywave signals from the lightning discharges in addition to the standard groundwave sferics. In approximately 1% of all waveforms, automated processing identified two 1-hop skywave reflection paths with delays indicative of an intracloud (height greater than 5 km) lightning source origin. For these events it was possible to determine both the height of the source above ground and the virtual reflection height of the ionosphere. Ionosphere heights agreed well with published values of 60 to 95 km with an expected diurnal variation. Source height determinations for 100,000+ intracloud lightning events ranged from 7 to 20 km AGL with negative-polarity events occurring above $15 km and positive-polarity events occurring below $15 km. The negativepolarity events are at a suprisingly high altitude and may be associated with discharges between the upper charge layer of a storm and a screening layer of charge above the storm. Approximately 100 of the intracloud events with LASA height determinations were also recorded by VHF receivers on the FORTE satellite. Independent FORTE source height estimates based on delays between direct and ground-reflected radio emissions showed excellent correlation with the VLF/LF estimates, but with a +1 km bias for the VLF/LF height determinations.

Acoustic waves with periods of 2–4 min and gravity waves with periods of 6–16 min have been detected at ionospheric heights (250–350 km) using GPS total electron content measurements. The area disturbed by these waves and the wave amplitudes have been associated with underlying thunderstorm activity. A statistical study comparing Next Generation Weather Radar thunderstorm measurements with ionospheric acoustic and gravity waves in the midlatitude U.S. Great Plains region was performed for the time period of May–July 2005. An increase of ionospheric acoustic wave disturbed area and amplitude is primarily associated with large thunderstorms (mesoscale convective systems). Ionospheric gravity wave disturbed area and amplitude scale with thunderstorm activity, with even small storms (i.e., individual storm cells) producing an increase of gravity waves.

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[1] This paper presents a new method for probing ionospheric D-layer fluctuations with time-domain very-low and low-frequency (VLF/LF) lightning waveforms detected several hundred kilometers away from lightning storms. The technique compares the amplitude and the time delay between the direct ground wave and the first-hop ionospheric reflection of the lightning signal to measure the apparent D-layer reflectivity and height. This time-domain technique allows a higher time and spatial resolution measurement of the D-layer fluctuations compared to previously reported frequency-domain techniques. For a region near a nighttime thunderstorm, results demonstrate that the apparent reflectivity and height exhibit significant variation on spatial scales of tens of kilometers and over time periods of hours. The range of the reflectivity variation was observed as large as 100% away from the averaged reflectivity for some localized regions, and the height varies by as much as 5% (4 km). The time scales and propagation velocities of the fluctuations appear to be consistent with signatures of atmospheric gravity waves at D-layer altitudes, and the direction of the fluctuation propagation suggests that the gravity waves are originated from the storm. Superimposed on the fluctuations, a general decreasing trend (by ∼4-8 km) in reflection height over the nighttime is observed. In some localized ionosphere regions, apparent splitting of the D-layer by 2-4 km is observed to last a short time period of about 10 min.

For shortcomings of poor exploaration and parameter complexities of the butterfly optimization algorithm, an improved butterfly optimization algorithm based the self-adaption method (SABOA) was proposed to extremely enhance the searching accuracy and the iteration capability. SABOA has advantages of having fewer parameters, the simple algorithm structure, and the strong precision. First, a new fragrance coefficient was added to the basic butterfly optimization algorithm. Then, new iteration and updating strategies were introduced in global searching and local searching phases. Finally, this paper tested different optimization problems including low-high functions and constrained problems, and the obtained results were compared with other well-known algorithms, this paper also drew various mathematical statistics figures to comprehensively analyze searching performances of the proposed algorithms. The experimental results show that SABOA can get less number of function evaluations compared to other considered algorithms, which illustrates that SABOA has great searching balance, large exploration, and high iterative speed. INDEX TERMS Butterfly optimization algorithm, global optimization, constrained problem. I. INTRODUCTION In applied mathematics and engineering fields, there are numerous optimization problems whose calculated solutions are in a large and complex searching space. Traditional optimization methods, including the steepest descent method, the conjugate gradient method, the variable scale method, and Newton method, can only deal with objective functions that are simple, continuously differentiable, and high order differentiable [1]-[3]. With the increasing of problem diversities and problem complexities, traditional optimization methods can not meet different requirements of higher calculation speed and lower average percentage error, so it is crucial to find for new optimization methods that have fast calculation speed and perfect convergence abilities [4], [5]. With the development of artificial intelligence, digitization, and computer technologies, numerous meta-heuristic optimization algorithms have been increasingly proposed and applied in science and engineering fields [6]-[8]. Meta-heuristic algorithms own characteristics of selforganizing, mutual compatibility, simplicity, parallelism, wholeness and harmony. Meta-heuristic algorithms work The associate editor coordinating the review of this manuscript and approving it for publication was Jagdish Chand Bansal.