# Morphological and Spectral Features of Ionospheric Structures at E- and F-Region Altitudes over Poker Flat Analyzed Using Modeling and Observations

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## Abstract

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## 1. Introduction

#### 1.1. Background

^{−1}) [28]. The spectral indices can be different for irregularities at different altitudes. For example, the spectral index values for high latitude F-region irregularities vary from 2.5 to 4.5, whereas the E-region spectral index values range from 1.5 to 3.2 [29]. Despite the studies mentioned here, a comparison between auroral E- and F-region irregularity spectra and the irregularity shapes had been missing, which motivates this study.

#### 1.2. Motivation

## 2. Data and Methodology

#### 2.1. Observational Data

#### 2.2. Modeling

_{0}depicts the axial ratio (AXR). ${{k}_{x}}^{\prime}$, ${{k}_{y}}^{\prime}$, and ${{k}_{z}}^{\prime}$ are the wave numbers in ${x}^{\prime}$, ${y}^{\prime}$, and ${z}^{\prime}$, respectively. ${z}^{\prime}$ and ${{k}_{z}}^{\prime}$ are along the magnetic field ${B}_{0}$, while the other two coordinates are in a plane perpendicular to ${B}_{0}$. k${}_{0}$ is the wave number associated with the outer scale l${}_{0}$. $\Delta N$ is the root-mean-square (RMS) of the electron density fluctuations, which are assumed to be generated by a zero-mean stationary random process. In the Hybrid spectrum, the irregularity distribution follows a power law in a plane perpendicular to the magnetic field and a Gaussian law along the magnetic field direction. The field lines are filled with plasma due to ionization in the auroral oval allowing the plasma distribution to be more like a Chapman distribution which could explain the Gaussian distribution along the field lines [27]. The symmetric nature of the Hybrid spectrum with respect to the magnetic field direction makes it suitable for modeling rod-like irregularities. Unlike the Hybrid, the Shkarofsky spectrum is a more generalized irregularity spectrum with a power-law distribution in all three directions that can be changed independently, allowing one to simulate rods, wings, and sheets for irregularity morphology. The Shkarofsky spectrum is given by

_{e}), drift speed $\left(\right|{v}_{d}\left|\right)$, and drift direction ($\angle {v}_{d}$) for a selected event are obtained from PFISR and SAGA. We perform SIGMA simulation over a 4D-grid space with four design variables, namely, N

_{e}, $|{v}_{d}|$, $\angle {v}_{d}$ and spectral index (SpInd), in addition to other five input parameters, namely, altitude (${\mathrm{H}}_{iono}$), no. of layers (${\mathrm{N}}_{l}$), layer thickness (${\mathrm{L}}_{th}$), axial ratio (AXR), and outer scale (${l}_{0}$), which we do not vary during one inverse run. In this study, we only use one irregularity layer, and the ${\mathrm{N}}_{l}$ parameter is not varied during the sensitivity analysis (discussed further). The initial range of values for the three design variables, namely, ${\mathrm{N}}_{e}$, $|{v}_{d}|$, and $\angle {v}_{d}$, are obtained from the auxiliary data. We consider a range of spectral index values from 2 to 6.

## 3. Results

_{e}and SpInd in Figure 6a and with respect to $|{v}_{d}|$ and $\angle {v}_{d}$ in Figure 6b. In these plots, we show the position of the global minimum ($\chi {{}^{\prime}}_{min}$) (magenta circle) and the median (yellow diamond) in the units of the standard deviation spread. Dashed lines indicate the confidence level contours, and the solid lines indicate the contours of $\chi {}^{\prime}$ values. The contour level associated with $\chi {}^{\prime}$ values close to 1 (area covered under the solid dark blue contour) shows the parametric space where the model simulations (simulated PSD) have a close match with the observations (observed PSD). The 90% confidence level contour indicated by the black dotted line shows a 90% chance that the true values of the design variables will fall within that region. A multi-dimensional optimization problem may have ambiguities associated with the solutions. These confidence interval plots are used to quantify ambiguities for the inverse runs we have performed.

_{0}) and the irregularity layer thickness (${\mathrm{L}}_{th}$) parameters. It is found that the scintillation strength increases as the irregularity thickness increases and decreases with the increase in the outer-scale length of the irregularities (figure not shown).

## 4. Discussion

#### 4.1. Morphology of the Irregularity Structures at E and F Heights

- The axial ratios estimated using our inverse analysis indicate that rod-like irregularity structures are more prominent for the E-region event (SAGA3 E-event from Table 2).
- Wing-type irregularity structures are likely responsible for the F-region phase fluctuations for both events (SAGA1 and SAGA2 F-events from Table 2).
- Additionally, the sensitivity analysis shown in Figure 5 support the results that the rod-like irregularities are responsible for E-region phase fluctuations and wing-like irregularities for F-region phase fluctuations.

#### 4.2. Variation of the Spectral Index at E- and F-Region Heights

- We analyzed spectral indices at irregularity layer height for the selected E- and F-region events. We found that the E-region power law index is less than those for the F-region cases (see Table 2);
- Spectral slopes of the PSDs of the phase time series on the ground are steeper at frequencies below 1 Hz compared to those above 1 Hz irrespective of E- or F-region scintillations (see Figure 7);
- The spectral slope of the scintillation spectrum on the ground is less than the spectral index at irregularity layer height.

## 5. Conclusions

- The axial ratio analyzed for the E-region event reveals that the irregularities are more elongated along the magnetic field lines having rod-like structures. On the other hand, the F-region irregularities have wing/sheet-like structures with irregularity axial ratios extending both along and across the field lines.
- The spectral indices analyzed at E- and F-region irregularity heights show that the E-region spectral index is less than the F-region spectral indices.
- Spectral slope analysis compares the slopes on the ground with those at the irregularity layer. We found that the spectral slopes on the ground are less than the slopes at the irregularity layer height for E- and F-region events, consistent with what is expected.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

GPS | Global Positioning System |

GNSS | Global Navigation Satellite System |

GDI | Gradient Drift Instability |

KHI | Kelvin-Helmholtz Instability |

MLT | Magnetic Local Time |

PSD | Power Spectral Density |

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**Figure 1.**Time series of detrended and filtered GPS signal phase ($\Phi {}_{f}$) for L1 C/A, (

**a**) PRN 25, an F-region event on 7 October 2015, (

**b**) PRN 1, an F-region event, and (

**c**) PRN 30, an E-region event, both on 16 November 2014. Data from all available SAGA receivers (IIT1, IIT3, etc.) during the scintillation interval are over-plotted for each event. (

**d**–

**f**) are the corresponding power spectral densities (PSD) for each event.

**Figure 2.**The sky plots of PFISR beam configuration (cyan squares) and the GPS satellites (solid red dots) (

**a**) PRN 25 for SAGA1 event, (

**b**) PRN 1 for SAGA2 event, and (

**c**) PRN 30 for SAGA3 (satellite path with a solid red dot marked as endpoint) events. (

**d**) Skyplot of PFISR beams and PRN 30 location for the SAGA 3 event is plotted over an all-sky image of 557.7 nm green line auroral emission during the scintillation interval.

**Figure 3.**Flow chart illustrates the SIGMA process to find the optimal input values. The number of irregularity layers used in this study is one (${\mathrm{N}}_{l}$ = 1). We perform inverse runs with SIGMA at two different heights—one at 120km (E-region) and another at 350km height (F-region). We convert the outer scale (${l}_{0}$) to outer scale wave number (${k}_{0}$) within SIGMA. We fix the inner scales (${r}_{0}$) to satisfy the Shkarofsky assumption that ${k}_{0}{r}_{0}<<1$ [1].

**Figure 4.**The observed and simulated PSD best fits for both Hybrid and Shkarofsky spectral models for the three events.

**Figure 5.**The SIGMA sensitivity analysis using the axial ratio parameter for all three events. The irregularity axial ratio representing wing-like structures fits well for F-region events and the axial ratio that represents rod-like structures best fits the E-region event.

**Figure 6.**Contours showing the confidence levels of four SIGMA design variables for the SAGA2 event.

**Figure 7.**Comparison of observed vs. simulated phase PSD slopes. The left columns (

**a**,

**c**,

**e**) represent the Hybrid spectrum, and the right columns (

**b**,

**d**,

**f**) represent the Shkarofsky spectrum for all three events. The slopes are computed for PSDs both at lower (below 1 Hz) and higher frequencies (above 1 Hz). The part inside the circles is considered noise.

**Figure 8.**(

**a**) Keograms of auroral brightness for E-region (SAGA3) event emitted by O, ${{\mathrm{N}}_{2}}^{+}$, H, and O at wavelengths of 557.7, 427.8, 486.1, and 630.0 nm, respectively. (

**b**) The variations of the local magnetic components (pink box highlights the scintillation time).

**Table 1.**A comparison of observed and simulated values of the propagation parameters. ${\mathrm{H}}_{iono}$ is 120 km (350 km) with a thickness of 10 km (50 km) for the E-region (F-region) event. We consider an outer scale of 15 km for all events. The drift direction estimates are measured counter-clockwise from the geomagnetic south. The SAGA drift estimates are shown in boldface.

SAGA1—F Event | SAGA2—F Event | SAGA3—E Event | ||||
---|---|---|---|---|---|---|

Parameter | Observed | Simulated | Observed | Simulated | Observed | Simulated |

Hybrid Spectrum | ||||||

${\mathrm{N}}_{e}$ (el/m^{3}) | (0.2–0.4) × 10^{12} | 0.2 × 10^{12} | (0.7–1.1) × 10^{12} | 0.75 × 10^{12} | (0.7–1.1) × 10^{12} | 1.05 × 10^{12} |

$|{v}_{d}|$ (m/s) | 1000–1500 (1500) | 1550 | 450–700 (500) | 550 | 500–800 | 500 |

$\angle {v}_{d}$ | 130${}^{\circ}$–200${}^{\circ}$ (140${}^{\circ}$) | 160${}^{\circ}$ | 290${}^{\circ}$–360${}^{\circ}$ (290${}^{\circ}$) | 300${}^{\circ}$ | 130${}^{\circ}$–200${}^{\circ}$ | 160${}^{\circ}$ |

Shkarofsky Spectrum | ||||||

${\mathrm{N}}_{e}$ (el/m^{3}) | (0.2–0.4) × 10^{12} | 0.27 × 10^{12} | (0.7–1.1) × 10^{12} | 1.05 × 10^{12} | (0.7–1.1) × 10^{12} | 0.74 × 10^{12} |

$|{v}_{d}|$ (m/s) | 1000–1500 (1500) | 1500 | 450–700 (500) | 500 | 500–800 | 825 |

$\angle {v}_{d}$ | 130${}^{\circ}$–200${}^{\circ}$ (140${}^{\circ}$) | 140${}^{\circ}$ | 290${}^{\circ}$–360${}^{\circ}$ (290${}^{\circ}$) | 290${}^{\circ}$ | 130${}^{\circ}$–200${}^{\circ}$ | 130${}^{\circ}$ |

SAGA1 F—Event | SAGA2 F—Event | SAGA3 E—Event | ||||
---|---|---|---|---|---|---|

Parameter | Hybrid | Shkarofsky | Hybrid | Shkarofsky | Hybrid | Shkarofsky |

Axial Ratio | 5 | a${}_{x}$ = 2, a${}_{y}$ = 1, a${}_{z}$ = 10 | 5 | a${}_{x}$ = 2, a${}_{y}$ = 1, a${}_{z}$ = 10 | 6 | a${}_{x}$ = 1, a${}_{y}$ = 1, a${}_{z}$ = 10 |

Wing-like | Wing-like | Rod-like | ||||

Spectral Index | 4.5 | 4.5 | 4 | 4.5 | 3 | 3.5 |

**Table 3.**The inverse analysis performed for three different irregularity structures (rods/wings/ sheets) for each of the three events. Underlined are the best fits.

SAGA1 F—Event | SAGA2 F—Event | SAGA3 E—Event | |
---|---|---|---|

Wings | ${\chi}^{\prime}=1.55$ | ${\chi}^{\prime}=1.82$ | ${\chi}^{\prime}=4.8$ |

Sheets | ${\chi}^{\prime}=7.21$ | ${\chi}^{\prime}=5.87$ | ${\chi}^{\prime}=5.2$ |

Rods | ${\chi}^{\prime}=3.2$ | ${\chi}^{\prime}=6.67$ | ${\chi}^{\prime}=1.43$ |

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## Share and Cite

**MDPI and ACS Style**

Vaggu, P.R.; Deshpande, K.B.; Datta-Barua, S.; Bust, G.S.; Hampton, D.L.; Rubio, A.L.; Conroy, J.P.
Morphological and Spectral Features of Ionospheric Structures at E- and F-Region Altitudes over Poker Flat Analyzed Using Modeling and Observations. *Sensors* **2023**, *23*, 2477.
https://doi.org/10.3390/s23052477

**AMA Style**

Vaggu PR, Deshpande KB, Datta-Barua S, Bust GS, Hampton DL, Rubio AL, Conroy JP.
Morphological and Spectral Features of Ionospheric Structures at E- and F-Region Altitudes over Poker Flat Analyzed Using Modeling and Observations. *Sensors*. 2023; 23(5):2477.
https://doi.org/10.3390/s23052477

**Chicago/Turabian Style**

Vaggu, Pralay Raj, Kshitija B. Deshpande, Seebany Datta-Barua, Gary S. Bust, Donald L. Hampton, Aurora López Rubio, and James P. Conroy.
2023. "Morphological and Spectral Features of Ionospheric Structures at E- and F-Region Altitudes over Poker Flat Analyzed Using Modeling and Observations" *Sensors* 23, no. 5: 2477.
https://doi.org/10.3390/s23052477