# Ionospheric Turbulence and the Equatorial Plasma Density Irregularities: Scaling Features and RODI

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data

## 3. Method and Analysis Results

## 4. Discussion

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ESA | European Space Agency |

BF | Bubble Flag |

GNSS | Global Navigation Satellite System |

GPS | Global Positioning System |

IBI | Swarm Level-2 Ionospheric Bubble Index |

PSD | Power Spectral density |

RODI | Rate Of change of electron Density Index |

## References

- Kil, H.; Heelis, R.A. Global distribution of density irregularities in the equatorial ionosphere. J. Geophys. Res.
**1998**, 103, 407–418. [Google Scholar] [CrossRef] - Woodman, R.F.; La Hoz, C. Radar observations of F region equatorial irregularities. J. Geophys. Res.
**1976**, 81, 5447–5466. [Google Scholar] [CrossRef] - Kelley, M. The Earth’s Ionosphere: Plasma Physics and Electrodynamics; International Geophysics, Elsevier Science: Amsterdam, The Netherlands, 2009. [Google Scholar]
- Schunk, R.W.; Nagy, A.F. Ionospheres: Physics, Plasma Physics, and Chemistry; Cambridge Atmospheric and Space Science Series; Cambridge University Press: Cambridge, UK, 2009. [Google Scholar]
- Cherniak, I.; Zakharenkova, I.; Sokolovsky, S. Multi-Instrumental Observation of Storm-Induced Ionospheric Plasma Bubbles at Equatorial and Middle Latitudes. J. Geophys. Res. Space Phys.
**2019**, 124, 1491–1508. [Google Scholar] [CrossRef] - Lühr, H.; Xiong, C.; Park, J.; Rauberg, J. Systematic study of intermediate-scale structures of equatorial plasma irregularities in the ionosphere based on CHAMP observations. Front. Phys.
**2014**, 2, 15. [Google Scholar] [CrossRef][Green Version] - Hysell, D.L.; Seyler, C.E. A renormalization group approach to estimation of anomalous diffusion in the unstable equatorial F region. J. Geophys. Res.
**1998**, 103, 26731–26738. [Google Scholar] [CrossRef] - Tsunoda, R.T.; Livingston, R.C.; McClure, J.P.; Hanson, W.B. Equatorial plasma bubbles: Vertically elongated wedges from the bottomside F layer. J. Geophys. Res.
**1982**, 87, 9171–9180. [Google Scholar] [CrossRef][Green Version] - Kil, H.; Heelis, R.A.; Paxton, L.J.; Oh, S.J. Formation of a plasma depletion shell in the equatorial ionosphere. J. Geophys. Res. Space Phys.
**2009**, 114, A11302. [Google Scholar] [CrossRef] - Tsunoda, R.T. Control of the seasonal and longitudinal occurrence of equatorial scintillations by the longitudinal gradient in integrated E region pedersen conductivity. J. Geophys. Res.
**1985**, 90, 447–456. [Google Scholar] [CrossRef] - Prikryl, P.; Jayachandran, P.T.; Mushini, S.C.; Chadwick, R. Climatology of GPS phase scintillation and HF radar backscatter for the high-latitude ionosphere under solar minimum conditions. Ann. Geophys.
**2011**, 29, 377–392. [Google Scholar] [CrossRef][Green Version] - Jin, Y.; Moen, J.I.; Miloch, W.J. GPS scintillation effects associated with polar cap patches and substorm auroral activity: Direct comparison. J. Space Weather. Space Clim.
**2014**, 4, A23. [Google Scholar] [CrossRef] - Jin, Y.; Moen, J.I.; Miloch, W.J. On the collocation of the cusp aurora and the GPS phase scintillation: A statistical study. J. Geophys. Res. Space Phys.
**2015**, 120, 9176–9191. [Google Scholar] [CrossRef] - Kintner, P.M.; Seyler, C.E. The status of observations and theory of high latitude ionospheric and magnetospheric plasma turbulence. Space Sci. Rev.
**1985**, 41, 91–129. [Google Scholar] [CrossRef] - Hysell, D.L.; Shume, E.B. Electrostatic plasma turbulence in the topside equatorial F region ionosphere. J. Geophys. Res. Space Phys.
**2002**, 107, 1269. [Google Scholar] [CrossRef][Green Version] - Hassam, A.B.; Hall, W.; Huba, J.D.; Keskinen, M.J. Spectral characteristics of interchange turbulence. J. Geophys. Res.
**1986**, 91, 13513–13522. [Google Scholar] [CrossRef] - Zargham, S.; Seyler, C.E. Collisional and inertial dynamics of the ionospheric interchange instability. J. Geophys. Res.
**1989**, 94, 9009–9027. [Google Scholar] [CrossRef] - Kraichnan, R.H. Inertial Ranges in Two-Dimensional Turbulence. Phys. Fluids
**1967**, 10, 1417–1423. [Google Scholar] [CrossRef][Green Version] - Kraichnan, R.H.; Montgomery, D. REVIEW ARTICLE: Two-dimensional turbulence. Rep. Prog. Phys.
**1980**, 43, 547–619. [Google Scholar] [CrossRef] - Yokoyama, T.; Shinagawa, H.; Jin, H. Nonlinear growth, bifurcation, and pinching of equatorial plasma bubble simulated by three-dimensional high-resolution bubble model. J. Geophys. Res. Space Phys.
**2014**, 119, 10474–10482. [Google Scholar] [CrossRef][Green Version] - Yokoyama, T. A review on the numerical simulation of equatorial plasma bubbles toward scintillation evaluation and forecasting. Prog. Earth Planet. Sci.
**2017**, 4, 37. [Google Scholar] [CrossRef] - Kelley, M.C. The Earth’s Ionosphere; Elsevier: Amsterdam, The Netherlands, 1989. [Google Scholar]
- Materassi, M.; Forte, B.; Coster, A.J.; Skone, S. (Eds.) The Dynamical Ionosphere; Elsevier: Amsterdam, The Netherlands, 2020. [Google Scholar]
- Tsunoda, R.T. High-latitude F-region irregularities: A review and synthesis. Rev. Geophys.
**1988**, 26, 719–760. [Google Scholar] [CrossRef][Green Version] - Sahr, J.D.; Fejer, B.G. Auroral electrojet plasma irregularity theory and experiment: A critical review of present understanding and future directions. J. Geophys. Res.
**1996**, 101, 26893–26910. [Google Scholar] [CrossRef] - Hysell, D.L. An overview and synthesis of plasma irregularities in equatorial spread /F. J. Atmos. Sol. Terr. Phys.
**2000**, 62, 1037–1056. [Google Scholar] [CrossRef] - Dyson, P.L.; McClure, J.P.; Hanson, W.B. In situ measurements of the spectral characteristics of F region ionospheric irregularities. J. Geophys. Res.
**1974**, 79, 1497. [Google Scholar] [CrossRef] - Livingston, R.C.; Rino, C.L.; McClure, J.P.; Hanson, W.B. Spectral characteristics of medium-scale equatorial F region irregularities. J. Geophys. Res.
**1981**, 86, 2421–2428. [Google Scholar] [CrossRef] - Cerisier, J.C.; Berthelier, J.J.; Beghin, C. Unstable density gradients in the high-latitude ionosphere. Radio Sci.
**1985**, 20, 755–761. [Google Scholar] [CrossRef] - Hobara, Y.; Lefeuvre, F.; Parrot, M.; Molchanov, O.A. Low-latitude ionospheric turbulence observed by Aureol-3 satellite. Ann. Geophys.
**2005**, 23, 1259–1270. [Google Scholar] [CrossRef][Green Version] - Xiong, C.; Stolle, C.; Lühr, H.; Park, J.; Fejer, B.G.; Kervalishvili, G.N. Scale analysis of equatorial plasma irregularities derived from Swarm constellation. Earth Planets Space
**2016**, 68, 121. [Google Scholar] [CrossRef] - Xiong, C.; Stolle, C.; Park, J. Climatology of GPS signal loss observed by Swarm satellites. Ann. Geophys.
**2018**, 36, 679–693. [Google Scholar] [CrossRef][Green Version] - Friis-Christensen, E.; Lühr, H.; Knudsen, D.; Haagmans, R. Swarm An Earth Observation Mission investigating Geospace. Adv. Space Res.
**2008**, 41, 210–216. [Google Scholar] [CrossRef] - Stolle, C.; Lühr, H.; Rother, M.; Balasis, G. Magnetic signatures of equatorial spread F as observed by the CHAMP satellite. J. Geophys. Res. Space Phys.
**2006**, 111, A02304. [Google Scholar] [CrossRef] - Xiong, C.; Lühr, H.; Ma, S.Y.; Stolle, C.; Fejer, B.G. Features of highly structured equatorial plasma irregularities deduced from CHAMP observations. Ann. Geophys.
**2012**, 30, 1259–1269. [Google Scholar] [CrossRef][Green Version] - Basu, S.; Basu, S. Equatorial scintillations: Advances since ISEA-6. J. Atmos. Terr. Phys.
**1985**, 47, 753–768. [Google Scholar] [CrossRef] - Kelley, M.C.; Makela, J.J.; Ledvina, B.M.; Kintner, P.M. Observations of equatorial spread-F from Haleakala, Hawaii. Geophys. Res. Lett.
**2002**, 29, 2003. [Google Scholar] [CrossRef] - Sahai, Y.; Fagundes, P.; Abalde, J.; Pimenta, A.; Bittencourt, J.; Otsuka, Y.; Rios, V. Generation of large-scale equatorial F-region plasma depletions during low range spread-F season. Ann. Geophys.
**2004**, 22, 15–23. [Google Scholar] [CrossRef][Green Version] - Hysell, D.L.; Burcham, J.D. JULIA radar studies of equatorial spread F. J. Geophys. Res. Space Phys.
**1998**, 103, 29155–29168. [Google Scholar] [CrossRef] - Huang, C.Y.; Burke, W.J.; Machuzak, J.S.; Gentile, L.C.; Sultan, P.J. Equatorial plasma bubbles observed by DMSP satellites during a full solar cycle: Toward a global climatology. J. Geophys. Res. Space Phys.
**2002**, 107, 1434. [Google Scholar] [CrossRef] - Burke, W.J.; Gentile, L.C.; Huang, C.Y.; Valladares, C.E.; Su, S.Y. Longitudinal variability of equatorial plasma bubbles observed by DMSP and ROCSAT-1. J. Geophys. Res. Space Phys.
**2004**, 109, A12301. [Google Scholar] [CrossRef] - Burke, W.; Huang, C.; Gentile, L.; Bauer, L. Seasonal-longitudinal variability of equatorial plasma bubbles. Ann. Geophys.
**2004**, 22, 3089–3098. [Google Scholar] [CrossRef][Green Version] - Su, S.Y.; Liu, C.H.; Ho, H.H.; Chao, C.K. Distribution characteristics of topside ionospheric density irregularities: Equatorial versus midlatitude regions. J. Geophys. Res. Space Phys.
**2006**, 111, A06305. [Google Scholar] [CrossRef] - Gentile, L.C.; Burke, W.J.; Rich, F.J. A climatology of equatorial plasma bubbles from DMSP 1989-2004. Radio Sci.
**2006**, 41. [Google Scholar] [CrossRef] - Gentile, L.C.; Burke, W.J.; Rich, F.J. A global climatology for equatorial plasma bubbles in the topside ionosphere. Ann. Geophys.
**2006**, 24, 163–172. [Google Scholar] [CrossRef] - Nishioka, M.; Saito, A.; Tsugawa, T. Occurrence characteristics of plasma bubble derived from global ground-based GPS receiver networks. J. Geophys. Res. Space Phys.
**2008**, 113. [Google Scholar] [CrossRef] - Park, J.; Noja, M.; Stolle, C.; Lühr, H. The Ionospheric Bubble Index deduced from magnetic field and plasma observations onboard Swarm. Earth Planets Space
**2013**, 65, 1333–1344. [Google Scholar] [CrossRef][Green Version] - Park, J.; Min, K.W.; Kim, V.P.; Kil, H.; Lee, J.J.; Kim, H.J.; Lee, E.; Lee, D.Y. Global distribution of equatorial plasma bubbles in the premidnight sector during solar maximum as observed by KOMPSAT-1 and Defense Meteorological Satellite Program F15. J. Geophys. Res. Space Phys.
**2005**, 110, A07308. [Google Scholar] [CrossRef][Green Version] - Whalen, J.A. Dependence of equatorial bubbles and bottomside spread F on season, magnetic activity, and E × B drift velocity during solar maximum. J. Geophys. Res. Space Phys.
**2002**, 107, 1024. [Google Scholar] [CrossRef] - De Michelis, P.; Consolini, G.; Tozzi, R. Magnetic field fluctuation features at Swarm’s altitude: A fractal approach. Geophys. Res. Lett.
**2015**, 42, 3100–3105. [Google Scholar] [CrossRef][Green Version] - Frisch, U. Turbulence: The Legacy of A.N. Kolmogorov; Cambridge University Press: Cambridge, UK, 1995. [Google Scholar]
- Consolini, G.; De Michelis, P.; Alberti, T.; Giannattasio, F.; Coco, I.; Tozzi, R.; Chang, T.T.S. On the Multifractal Features of Low-Frequency Magnetic Field Fluctuations in the Field-Aligned Current Ionospheric Polar Regions: Swarm Observations. J. Geophys. Res. Space Phys.
**2020**, 125, e27429. [Google Scholar] [CrossRef] - Davis, A.; Marshak, A.; Wiscombe, W.; Cahalan, R. Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated. J. Geophys. Res. Space Phys.
**1994**, 99, 8055–8072. [Google Scholar] [CrossRef] - Basu, S.; MacKenzie, E.; Basu, S.; Coley, W.R.; Sharber, J.R.; Hoegy, W.R. Plasma structuring by the gradient drift instability at high latitudes and comparison with velocity shear driven processes. J. Geophys. Res. Space Phys.
**1990**, 95, 7799–7818. [Google Scholar] [CrossRef] - Kraichnan, R.H. On Kolmogorov’s inertial-range theories. J. Fluid Mech.
**1974**, 62, 305–330. [Google Scholar] [CrossRef][Green Version] - Monin, A.S.; Yaglom, A.M. Statistical Fluid Mechanics: Mechanics of Turbulence; MIT Press: Cambridge, MA, USA, 1975. [Google Scholar]
- Rose, H.A.; Sulem, P.L. Fully developed turbulence and statistical mechanics. J. Phys.
**1978**, 39, 1938–1943. [Google Scholar] [CrossRef] - De Michelis, P.; Pignalberi, A.; Consolini, G.; Coco, I.; Tozzi, R.; Pezzopane, M.; Giannattasio, F.; Balasis, G. On the 2015 St. Patrick’s Storm Turbulent State of the Ionosphere: Hints From the Swarm Mission. J. Geophys. Res. Space Phys.
**2020**, 125, e27934. [Google Scholar] [CrossRef] - Pignalberi, A. TITIPy: A python tool for the calculation and mapping of topside ionosphere turbulence indices. Comput. Geosci.
**2021**, 104675. [Google Scholar] [CrossRef] - Jin, Y.; Spicher, A.; Xiong, C.; Clausen, L.B.N.; Kervalishvili, G.; Stolle, C.; Miloch, W.J. Ionospheric Plasma Irregularities Characterized by the Swarm Satellites: Statistics at High Latitudes. J. Geophys. Res. Space Phys.
**2019**, 124, 1262–1282. [Google Scholar] [CrossRef] - Piersanti, M.; De Michelis, P.; Del Moro, D.; Tozzi, R.; Pezzopane, M.; Consolini, G.; Marcucci, M.F.; Laurenza, M.; Di Matteo, S.; Pignalberi, A.; et al. From the Sun to Earth: Effects of the 25 August 2018 geomagnetic storm. Ann. Geophys.
**2020**, 38, 703–724. [Google Scholar] [CrossRef] - Chang, T.S. An Introduction to Space Plasma Complexity; Cambridge University Press: Cambridge, UK, 2015. [Google Scholar]
- Wu, C.C.; Chang, T. Dynamical evolution of coherent structures in intermittent two-dimensional MHD turbulence. IEEE Trans. Plasma Sci.
**2000**, 28, 1938–1943. [Google Scholar] [CrossRef] - Chang, T.; Tam, S.W.Y.; Wu, C.C. Complexity induced anisotropic bimodal intermittent turbulence in space plasmas. Phys. Plasmas
**2004**, 11, 1287–1299. [Google Scholar] [CrossRef][Green Version] - Pécseli, H.L. Spectral properties of electrostatic drift wave turbulence in the laboratory and the ionosphere. Ann. Geophys.
**2015**, 33, 875–900. [Google Scholar] [CrossRef]

**Figure 1.**

**Top panel**: Global accumulated plot of ${N}_{e}$ values as recorded on board Swarm A from April 2014 to 31 January 2016, for $Kp\le 3$ and between 18:00 and 24:00 LT.

**Bottom panel**: Accumulated plot of the subset of ${N}_{e}$ values corresponding to IBI = 1 and BF = 1, and therefore to the presence of plasma bubbles, over the same time interval considered in the top panel.

**Figure 2.**(

**Top**): $\gamma \left(2\right)$ values associated with electron density data selected according to the following conditions: 18:00–24:00 LT, $\pm {40}^{\circ}$ geographic latitude, $Kp\le 3$ in the latitude–longitude plane (

**left**) and corresponding probability density (

**right**). (

**Bottom**): $\gamma \left(2\right)$ values for electron density data associated with plasma bubbles in the latitude–longitude plane (

**left**) and corresponding probability density (

**right**).

**Figure 3.**(

**Top**): Intermittency values for electron density data selected under the following conditions: 18:00–24:00 LT, $\pm {40}^{\circ}$ geographic latitude, and $Kp\le 3$ in the latitude–longitude plane (

**left**) and corresponding probability density (

**right**). (

**Bottom**): Intermittency values for electron density data associated with plasma bubbles in the latitude–longitude plane (

**left**) and corresponding probability density (

**right**).

**Figure 4.**(

**Top**): Rate of change Of electron Density Index (RODI) values associated with electron density data selected under the following conditions: 18:00–24:00 LT, $\pm {40}^{\circ}$ geographic latitude, and $Kp\le 3$ in the latitude–longitude plane (

**left**) and corresponding probability density (

**right**). (

**Bottom**): RODI values associated with the plasma bubbles in the latitude–longitude plane (

**left**) and corresponding probability density (

**right**).

**Figure 5.**Joint probability densities between RODI and $\gamma \left(2\right)$ (on the

**left**) and between RODI and Intermittency (on the

**right**) inside plasma bubbles.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

De Michelis, P.; Consolini, G.; Tozzi, R.; Pignalberi, A.; Pezzopane, M.; Coco, I.; Giannattasio, F.; Marcucci, M.F. Ionospheric Turbulence and the Equatorial Plasma Density Irregularities: Scaling Features and RODI. *Remote Sens.* **2021**, *13*, 759.
https://doi.org/10.3390/rs13040759

**AMA Style**

De Michelis P, Consolini G, Tozzi R, Pignalberi A, Pezzopane M, Coco I, Giannattasio F, Marcucci MF. Ionospheric Turbulence and the Equatorial Plasma Density Irregularities: Scaling Features and RODI. *Remote Sensing*. 2021; 13(4):759.
https://doi.org/10.3390/rs13040759

**Chicago/Turabian Style**

De Michelis, Paola, Giuseppe Consolini, Roberta Tozzi, Alessio Pignalberi, Michael Pezzopane, Igino Coco, Fabio Giannattasio, and Maria Federica Marcucci. 2021. "Ionospheric Turbulence and the Equatorial Plasma Density Irregularities: Scaling Features and RODI" *Remote Sensing* 13, no. 4: 759.
https://doi.org/10.3390/rs13040759