Articles | Volume 38, issue 2
https://doi.org/10.5194/angeo-38-445-2020
© Author(s) 2020. This work is distributed under
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the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/angeo-38-445-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Regular paper
| 
03 Apr 2020
Regular paper |
| 03 Apr 2020
| 03 Apr 2020
Structural characterization of the equatorial F region plasma irregularities in the multifractal context
Neelakshi Joshi
CORRESPONDING AUTHOR
Computational Space Physics Group, Lab for Computing and Applied Math (LABAC), National Institute for Space Research (INPE), Av. dos Astronautas, 1758, São José dos Campos, São Paulo 12227-690, Brazil
Reinaldo R. Rosa
Computational Space Physics Group, Lab for Computing and Applied Math (LABAC), National Institute for Space Research (INPE), Av. dos Astronautas, 1758, São José dos Campos, São Paulo 12227-690, Brazil
Siomel Savio
Aeronomy Division, National Institute for Space Research (INPE), Av. dos Astronautas, 1758, São José dos Campos, São Paulo 12227-690, Brazil
China-Brazil Joint Laboratory for Space Weather, NSSC/INPE, Av. dos Astronautas, 1758, São José dos Campos, São Paulo 12227-690, Brazil
Esfhan Alam Kherani
Aeronomy Division, National Institute for Space Research (INPE), Av. dos Astronautas, 1758, São José dos Campos, São Paulo 12227-690, Brazil
Francisco Carlos de Meneses
Aeronomy Division, National Institute for Space Research (INPE), Av. dos Astronautas, 1758, São José dos Campos, São Paulo 12227-690, Brazil
School of Physics and Mathematics, Autonomous University of Nuevo León (UANL), Av. Universidad s/n, Cd. Universitaria, San Nicolás de los Garza, N.L. 66455, Mexico
Stephan Stephany
Computational Space Physics Group, Lab for Computing and Applied Math (LABAC), National Institute for Space Research (INPE), Av. dos Astronautas, 1758, São José dos Campos, São Paulo 12227-690, Brazil
Polinaya Muralikrishna
Aeronomy Division, National Institute for Space Research (INPE), Av. dos Astronautas, 1758, São José dos Campos, São Paulo 12227-690, Brazil
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Lalit Mohan Joshi, Samireddipelle Sripathi, Muppidi Ravi Kumar, and Esfhan Alam Kherani
Ann. Geophys., 36, 25–35, https://doi.org/10.5194/angeo-36-25-2018, https://doi.org/10.5194/angeo-36-25-2018, 2018
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This work deals with the theoretical investigation of the inherent north&endash;south asymmetry in the ionospheric response to seismic infrasound. Magnetic field parallel component of the wind vector associated with the seismic infrasound varies significantly in the north–south direction due to the variation in the inclination of the Earth's magnetic field. This and other related aspects have been investigate using the physics-based ionospheric model.
R. Y. C. Cueva, E. R. de Paula, and A. E. Kherani
Ann. Geophys., 31, 2137–2146, https://doi.org/10.5194/angeo-31-2137-2013, https://doi.org/10.5194/angeo-31-2137-2013, 2013
Related subject area
Subject: Earth's ionosphere & aeronomy | Keywords: Ionospheric irregularities
Temporal and altitudinal variability of the spread F observed by the VHF radar over Christmas Island
Effect of neutral winds on the creation of non-specular meteor trail echoes
Simultaneous ground-based and in situ Swarm observations of equatorial F-region irregularities over Jicamarca
Occurrence climatology of equatorial plasma bubbles derived using FormoSat-3 ∕ COSMIC GPS radio occultation data
Localized total electron content enhancements in the Southern Hemisphere
Stratification observed by the in situ plasma density measurements from the Swarm satellites
Traits of sub-kilometre F-region irregularities as seen with the Swarm satellites
Equatorial plasma bubbles developing around sunrise observed by an all-sky imager and global navigation satellite system network during storm time
Investigation of the relationship between the spatial gradient of total electron content (TEC) between two nearby stations and the occurrence of ionospheric irregularities
Research on small-scale structures of ice particle density and electron density in the mesopause region
On developing a new ionospheric plasma index for Brazilian equatorial F region irregularities
Observation of seasonal asymmetry in the range spread F occurrence at different longitudes during low and moderate solar activity
Identifying a possible stratification phenomenon in ionospheric F2 layer using the data observed by the DEMETER satellite: method and results
Global sounding of F region irregularities by COSMIC during a geomagnetic storm
On the convection of ionospheric density features
The ionospheric response over the UK to major bombing raids during World War II
Ricardo Yvan de La Cruz Cueva, Eurico Rodrigues de Paula, and Acácio Cunha Neto
Ann. Geophys., 40, 563–570, https://doi.org/10.5194/angeo-40-563-2022, https://doi.org/10.5194/angeo-40-563-2022, 2022
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This paper brings analysis of spread-F echoes along the years of 2003 to 2012 from Christmas Island radar. We organize our data with the objective of observing the peak time and altitude distribution. Our results indicate the peak time occurrence of echoes to be distributed closer to local sunset during solar maximum and around midnight during solar minimum; meanwhile, the peak altitude echoes show higher altitude occurrences during solar maxima and lower altitudes during solar minima.
Freddy Galindo, Julio Urbina, and Lars Dyrud
Ann. Geophys., 39, 709–719, https://doi.org/10.5194/angeo-39-709-2021, https://doi.org/10.5194/angeo-39-709-2021, 2021
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Micro-size particles entering the Earth’s atmosphere do not emit enough light to be observed as meteors, but they can be probed with radars. The echo from these meteors depends on particle size and the atmosphere in which the particle travels. In this paper, we study the importance of neutral winds in forming meteor returns sensed by radars. We show that meteor trails can exhibit unique radar signatures due to neutral winds, explaining unique signatures in radar maps.
Sharon Aol, Stephan Buchert, Edward Jurua, and Marco Milla
Ann. Geophys., 38, 1063–1080, https://doi.org/10.5194/angeo-38-1063-2020, https://doi.org/10.5194/angeo-38-1063-2020, 2020
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Ionospheric irregularities are a common phenomenon in the low-latitude ionosphere. In this paper, we compared simultaneous observations of plasma plumes by the JULIA radar, ionogram spread F generated from ionosonde observations installed at the Jicamarca Radio Observatory, and irregularities observed in situ by Swarm to determine whether Swarm in situ observations can be used as indicators of the presence of plasma plumes and spread F on the ground.
Ankur Kepkar, Christina Arras, Jens Wickert, Harald Schuh, Mahdi Alizadeh, and Lung-Chih Tsai
Ann. Geophys., 38, 611–623, https://doi.org/10.5194/angeo-38-611-2020, https://doi.org/10.5194/angeo-38-611-2020, 2020
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The paper focuses on the analyses of the global occurrence of equatorial plasma bubble events using S4 data that were calculated from GPS radio occultation measurements of the FormoSat-3/COSMIC mission. The advantage in using radio occultation data is that we get information not only on the occurrence and intensity of the equatorial bubble events, but also on the altitude distribution. We analyzed a 10.5-year time series of COSMIC data and demonstrated a strong dependence on the solar cycle.
Ilya K. Edemskiy
Ann. Geophys., 38, 591–601, https://doi.org/10.5194/angeo-38-591-2020, https://doi.org/10.5194/angeo-38-591-2020, 2020
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This paper investigates a feature in the Southern Hemisphere ionosphere that is observed near midday in the form of a localized enhancement of the electron density. After being discovered in global ionospheric maps, the enhancements were also observed via in situ measurements of the electron concentration. The probability of detecting an enhancement is maximal during the autumn–winter period and does not seem to be directly dependent on geomagnetic indices or solar wind parameters.
Xiuying Wang, Wanli Cheng, Zihan Zhou, Dehe Yang, Jing Cui, and Feng Guo
Ann. Geophys., 38, 517–526, https://doi.org/10.5194/angeo-38-517-2020, https://doi.org/10.5194/angeo-38-517-2020, 2020
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To get the global distribution of the stratification phenomenon, the in situ plasma density measurements, obtained by the Swarm satellites orbiting at different altitudes above the F2 peak, are used to study this phenomenon. The continuous morphology of this phenomenon and its features along the latitudinal direction are obtained, and a new discovery from the in situ measurements is the stratification on southern mid-latitudes.
Sharon Aol, Stephan Buchert, and Edward Jurua
Ann. Geophys., 38, 243–261, https://doi.org/10.5194/angeo-38-243-2020, https://doi.org/10.5194/angeo-38-243-2020, 2020
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During the night, in the F region, equatorial ionospheric irregularities manifest as plasma depletions observed by satellites and may cause radio signals to fluctuate. We checked the distribution traits of ionospheric F-region irregularities in the low latitudes using 16 Hz electron density observations made by the faceplate onboard Swarm satellites. Using the high-resolution faceplate data, we were able to identify ionospheric irregularities of scales of only a few hundred metres.
Kun Wu, Jiyao Xu, Xinan Yue, Chao Xiong, Wenbin Wang, Wei Yuan, Chi Wang, Yajun Zhu, and Ji Luo
Ann. Geophys., 38, 163–177, https://doi.org/10.5194/angeo-38-163-2020, https://doi.org/10.5194/angeo-38-163-2020, 2020
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An equatorial plasma bubble (EPB) event, emerging near dawn and developing after sunrise, was simultaneously observed by an all-sky imager and the global navigation satellite system (GNSS) network. The observed EPBs showed westward drifts, different from post-sunset EPBs. The EPBs occurred in the recovery phase of a geomagnetic storm, possibly playing a key role in initializing their developments. The results provide a new perspective of EPBs, enriching our knowledge of ionospheric irregularity.
Teshome Dugassa, John Bosco Habarulema, and Melessew Nigussie
Ann. Geophys., 37, 1161–1180, https://doi.org/10.5194/angeo-37-1161-2019, https://doi.org/10.5194/angeo-37-1161-2019, 2019
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The relation between the occurrence of ionospheric irregularities and the spatial gradient of TEC derived from two closely located stations, located within the equatorial region over Ethiopia, was investigated. The relationship between σ(∆TEC/∆long) and ROTIave correlate linearly with correlation coefficients of C = 0.7975 and C = 0.7915 over ASAB and DEBK, respectively. In addition to latitudinal gradients, the longitudinal gradient of TEC has a significant contribution to the TEC fluctuations.
Ruihuan Tian, Jian Wu, Jinxiu Ma, Yonggan Liang, Hui Li, Chengxun Yuan, Yongyuan Jiang, and Zhongxiang Zhou
Ann. Geophys., 37, 1079–1094, https://doi.org/10.5194/angeo-37-1079-2019, https://doi.org/10.5194/angeo-37-1079-2019, 2019
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The density distribution of ice particles and electrons near the boundary of the polar mesosphere summer echo (PMSE) region is studied. The results show that when the radius distribution function of the condensation nucleus is a Gaussian type, for a certain range of the condensation core radius, sharp peaks with a meter scale appear in the density profiles of ice particles and electrons. These small-scale structures of electron density may be one of the causes of the PMSE phenomenon.
Laysa Cristina Araujo Resende, Clezio Marcos Denardini, Giorgio Arlan Silva Picanço, Juliano Moro, Diego Barros, Cosme Alexandre Oliveira Barros Figueiredo, and Régia Pereira Silva
Ann. Geophys., 37, 807–818, https://doi.org/10.5194/angeo-37-807-2019, https://doi.org/10.5194/angeo-37-807-2019, 2019
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The Brazilian Space Weather Study and Monitoring Program (Embrace) has been developing different indexes that describe ionospheric effects in the Brazilian sector. The main purpose of this work was to produce a new ionospheric scale based on the analysis of the ionospheric plasma drift velocity. We analyzed 7 years of data in order to construct a standardized scale. The results of this new index allow us to evaluate the impacts of ionospheric phenomena in the space weather environment.
Abimbola O. Afolayan, Mandeep Jit Singh, Mardina Abdullah, Suhaila M. Buhari, Tatsuhiro Yokoyama, and Pornchai Supnithi
Ann. Geophys., 37, 733–745, https://doi.org/10.5194/angeo-37-733-2019, https://doi.org/10.5194/angeo-37-733-2019, 2019
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The equatorial spread F (ESF) is a nighttime phenomenon that can have a deleterious effect on the radio communication system. We investigated the parameters influencing the seasonal morphology of the range type spread F (RSF) using ionosonde data from different longitude sectors. The observed RSF occurrence features showed distinct patterns across these sectors, including seasonal asymmetry. This asymmetry was attributed to the probable effect of the zonal wind reversal and gravity waves.
Xiuying Wang, Dehe Yang, Dapeng Liu, and Wei Chu
Ann. Geophys., 37, 645–655, https://doi.org/10.5194/angeo-37-645-2019, https://doi.org/10.5194/angeo-37-645-2019, 2019
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To check the difference between data observed at different altitudes of the DEMETER satellite, a statistical method is adopted to evaluate whether data difference is caused by normal data fluctuation or by altitude adjustment. Based on the method, in situ electron density data at higher altitudes are found to be greater than those at lower altitudes. We speculate that this phenomenon is caused by stratification above F2 peak region. The proposed method is useful when comparing fluctuated data.
Klemens Hocke, Huixin Liu, Nicholas Pedatella, and Guanyi Ma
Ann. Geophys., 37, 235–242, https://doi.org/10.5194/angeo-37-235-2019, https://doi.org/10.5194/angeo-37-235-2019, 2019
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The GPS radio occultation data of the COSMIC-FORMOSAT-3 mission are used to visualize the global distribution of ionospheric irregularities in the F2 region during a geomagnetic storm, at solar minimum, and at solar maximum.
John D. de Boer, Jean-Marc A. Noël, and Jean-Pierre St.-Maurice
Ann. Geophys., 37, 201–214, https://doi.org/10.5194/angeo-37-201-2019, https://doi.org/10.5194/angeo-37-201-2019, 2019
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Modelling aurorae, we asked what boundary condition (BC) to use for the E field on the upper boundary. Typically a Dirichlet BC is used, since processes above the domain generate E. But then conductivity structures trigger FACs driven immediately by magnetospheric convection, even though it is a finite energy source, delayed by the Alfvén speed. If the BC is not ideal, then E x B drift in the ionosphere depends on the plasma's properties. So we investigated.
Christopher J. Scott and Patrick Major
Ann. Geophys., 36, 1243–1254, https://doi.org/10.5194/angeo-36-1243-2018, https://doi.org/10.5194/angeo-36-1243-2018, 2018
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The variability of the Earth's ionosphere (the electrified region of the Earth's upper atmosphere) results from external forcing from above (through solar activity and space weather effects) and from below (via natural sources such as lightning storms and tectonics). Bombing raids over Europe during World War II were used to determine the quantitative impact of explosions on the ionosphere. It was found that raids using more than 300 tonnes of explosives weakened the ionosphere for up to 5 h.
Cited articles
Abdu, M. A., Nogueira, P. A. B., Santos, A. M., de Souza, J. R., Batista, I. S., and Sobral, J. H. A.: Impact of disturbance electric fields in the evening on prereversal vertical drift and spread F developments in the equatorial ionosphere, Ann. Geophys., 36, 609–620, https://doi.org/10.5194/angeo-36-609-2018, 2018. a
Abramenko, V. I., Yurchyshyn, V. B., Wang, H., Spirock, T. J., and Goode, P. R.: Scaling behavior of structure functions of the longitudinal magnetic field in active regions of the Sun,
Astrophys. J., 577, 487–495,
https://doi.org/10.1086/342169, 2002. a
Alimov, V. A., Vybornov, F. I., and Rakhlin, A. V.: Multifractal Structure of Intermittency in a Developed Ionospheric Turbulence,
Radiophys. Quantum. El., 51, 438, https://doi.org/10.1007/s11141-008-9044-4, 2008. a
Cander, L. R.: Ionospheric Space Weather Targets, in: Ionospheric Space Weather, Springer International Publishing, 245–264,
https://doi.org/10.1007/978-3-319-99331-7_9, 2019. a
Carbone, V., Bruno, R., and Veltri, P.: Scaling laws in the solar wind turbulence, in: Small-Scale Structures in Three-Dimensional Hydrodynamic and Magnetohydrodynamic Turbulence, edited by: Meneguzzi, M., Pouquet, A., and Sulem, P. L.,
Lect. Notes Phys., 462, 153–158,
https://doi.org/10.1007/BFb0102411, 1995. a
Chian, A. C.-L. and Muñoz, P. R.: Detection of current sheets and magnetic reconnections at the turbulent leading edge of an interplanetary coronal mass ejection, Astrophys. J. Lett., 733, L34, https://doi.org/10.1088/2041-8205/733/2/l34, 2011. a
Chian, A. C.-L., Abalde, J. R., Miranda, R. A., Borotto, F. A., Hysell, D. L., Rempel, E. L., and Ruffolo, D.: Multi-spectral optical imaging of the spatiotemporal dynamics of ionospheric intermittent turbulence, Sci. Rep., 8, 10568, doi:10.1038/s41598-018-28780-5, 2018. a
Costa, E. and Kelley, M. C.: On the role of steepened structures and drift waves in equatorial spread F, J. Geophys. Res., 83, 4359–4364, https://doi.org/10.1029/JA083iA09p04359, 1978. a
de Freitas, D. B., Nepomuceno, M. M. F., de Moraes Junior, P. R. V., Lopes, C. E. F., Das Chagas, M. L., Bravo, J. P., Costa, A. D., Canto Martins, B. L., De Medeiros, J. R., and Leão, I. C.: New suns in the cosmos, III. Multifractal signature analysis,
Astrophys. J., 831, 87, https://doi.org/10.3847/0004-637x/831/1/87, 2016. a
Dyrud, L., Krane, B., Oppenheim, M., P/'ecseli, H. L., Trulsen, J., and Wernik, A. W.: Structure functions and intermittency in ionospheric plasma turbulence,
Nonlinear Proc. Geoph., 15, 847–862, 2008. a
Fornari, G., Rosa, R., De Meneses, F. C., and Muralikrishna, P.: Spectral fluctuation analysis of ionospheric inhomogeneities over Brazilian territory, Part I: Equatorial F-region plasma bubbles, Adv. Space Res., 58, 2037–2042, https://doi.org/10.1016/j.asr.2016.03.039, 2016. a
Grauer, R., Krug, J., and Marliani, C.: Scaling of high-order structure functions in magnetohydrodynamic turbulence, Phys. Lett. A, 195, 335–338, https://doi.org/10.1016/0375-9601(94)90038-8, 1994. a
Grech, D.: Alternative measure of multifractal content and its application in finance, Chaos. Soliton. Fract., 88, 183–195, https://doi.org/10.1016/j.chaos.2016.02.017, 2016 a
Hysell, D. L., Kelley, M. C., Swartz, W. E., Pfaff, R. F., and Swenson, C. M.: Steepened structures in equatorial spread F: 1. New observations, J. Geophys. Res., 99, 8827–8840, https://doi.org/10.1029/93JA02961, 1994. a
Hysell, D. L., Seyler, C. E., and Kelley, M. C.: Steepened structures in equatorial spread F: 2. Theory, J. Geophys. Res., 99, 8841–8850, https://doi.org/10.1029/93JA02960, 1994. a
Biblioteca, National Institute for Space Research (INPE):
Structural characterization of the equatorial F region plasma irregularities in the multifractal context, available at: http://urlib.net/rep/8JMKD3MGP3W34R/803U8PQA8
last access: 17 October 2019. a
Kantelhardt, J. W. and Meyers, R. A. (Eds.): Fractal and multifractal time series, Encyclopedia of complexity and systems science, Springer New York, 3754–3779, https://doi.org/10.1007/978-0-387-30440-3_221, 2009. a
Kelley, M. C., Seyler, C. E., and Zargham, S.: Collisional interchange instability: 2. A comparison of the numerical simulations with the in situ experimental data, J. Geophys. Res., 92, 10089–10094, https://doi.org/10.1029/JA092iA09p10089, 1987. a
Kelley, M. C. and Hysell, D. L.: Equatorial Spread-F and neutral atmospheric turbulence: A review and a comparative anatomy,
J. Atmos. Terr. Phys., 53, 695–708
https://doi.org/10.1016/0021-9169(91)90122-N, 1991. a
Kelley, M. C., Ilma, R. R., and Crowley, G.: On the origin of pre-reversal enhancement of the zonal equatorial electric field, Ann. Geophys., 27, 2053–2056, https://doi.org/10.5194/angeo-27-2053-2009, 2009. a
Li, G., Ning, B., Liu, L., Ren, Z., Lei, J., and Su, S.-Y.: The correlation of longitudinal/seasonal variations of evening equatorial pre-reversal drift and of plasma bubbles, Ann. Geophys., 25, 2571–2578, https://doi.org/10.5194/angeo-25-2571-2007, 2007. a
Lu, X., Zhao, H., Lin, H., and Wu, Q.: Multifractal Analysis for Soft Fault Feature Extraction of Nonlinear Analog Circuits, Math. Probl. Eng., 2016, 7305702, https://doi.org/10.1155/2016/7305702, 2016. a
Macek, W. M.: Multifractality and intermittency in the solar wind,
Nonlinear Proc. Geoph., 14, 695–700, 2007. a
Makowiec, D., Rynkiewicz, A., Gałaska, R., Wdowczyk-Szulc, J., and Żarczyńska-Buchowiecka, M.: Reading multifractal spectra: Aging by multifractal analysis of heart rate, Europhys. Lett., 94, 68005, https://doi.org/10.1209/0295-5075/94/68005, 2011. a
Miranda, R. A., Chian, A. C.-L., and Rempel, E. L.: Universal scaling laws for fully-developed magnetic field turbulence near and far upstream of the Earth’s bow shock, Adv. Space Res., 51, 1893,
https://doi.org/10.1016/j.asr.2012.03.007, 2013. a
Muralikrishna, P. and Vieira, L. P.: Equatorial F-region irregularities generated by the Rayleigh-Taylor instability mechanism: rocket observations from Brazil,
Rev. Bras. Geof., 25, 6, https://doi.org/10.1590/S0102-261X2007000600016, 2007. a, b, c
Neelakshi, J., Rosa, R. R., Savio, S., De Meneses, F. C., Stephany, S., Fornari, G., and Muralikrishna, P.: Spectral fluctuation analysis of ionospheric inhomogeneities over Brazilian territory, Part II: E-F valley region plasma instabilities,
Adv. Space Res., 64, 1592–1599, https://doi.org/10.1016/j.asr.2019.07.015, 2019. a
Peng, C. K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., and Goldberger, A. L.: Mosaic organization of DNA nucleotides, Phys. Rev. E, 49, 1685–1689, https://doi.org/10.1103/PhysRevE.49.1685, 1994. a
Savio, S., Muralikrishna, P., Batista, I. S., and de Meneses, F. C.: Wave structures observed in the equatorial F-region plasma density and temperature during the sunset period, Adv. Space Res., 58, 2043–2051, https://doi.org/10.1016/j.asr.2016.07.026, 2016. a, b, c
Savio, S., Sousasantos, J., Pimenta, A. A., Yang, G., Kherani, E. A., Wang, C., and Liu, Z.: Quasiperiodic rising structures in the E-F valley region below the equatorial plasma bubble: A numerical study,
J. Geophys. Res.-Space, 124, 7247–7255, https://doi.org/10.1029/2019JA026620, 2019.
Seuront, L., Schmitt, F., Lagadeuc, Y., Schertzer, D., and Lovejoy, S.: Universal multifractal analysis as a tool to characterize multiscale intermittent patterns: example of phytoplankton distribution in turbulent coastal waters,
J. Plankton Res., 21, 877–922, 1999.
Sivavaraprasad, G., Otsuka, Y., Tripathi, N. K., Chowdhary, V. R., Ratnam, D. V., and Khan, M. A.: Spatial and temporal characteristics of ionospheric total electron content over Indian equatorial and low-latitude GNSS stations,
Conference on Signal Processing And Communication Engineering Systems (SPACES), Vijayawada, 105–108,
https://doi.org/10.1109/SPACES.2018.8316326, 2018. a, b
Telesca, L. and Lovallo, M.: Revealing competitive behaviours in music by means of the multifractal detrended fluctuation analysis: application to Bach's Sinfonias,
P. Roy. Soc. A-Math. Phy., 467, 3022–3032,
https://doi.org/10.1098/rspa.2011.0118, 2011. a
Wawrzaszek, A. and Macek, W. M.: Observation of the multifractal spectrum in solar wind turbulence by Ulysses at high latitudes, J. Geophys. Res., 115, A07104, doi:10.1029/2009JA015176, 2010. a
Wawrzaszek, A., Echim, M. and Bruno, R.: Multifractal Analysis of Heliospheric Magnetic Field Fluctuations Observed by Ulysses,
Astrophys. J., 876, 153, https://doi.org/10.3847/1538-4357/ab1750, 2019. a
Zargham, S. and Seyler, C. E.: Collisional interchange instability: 1. Numerical simulations of intermediate‐scale irregularities, J. Geophys. Res., 92, 10073–10088, https://doi.org/10.1029/JA092iA09p10073, 1987. a
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