# Latitudinal Dependence of the Ionospheric Slab Thickness for Estimation of Ionospheric Response to Geomagnetic Storms

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}change was masked by the overall prolonged electron density increase during 21–31 March. The multiple correlation analysis revealed the latitudinal dependence of dominant Space Weather parameters’ impacts on foF2.

## 1. Introduction

^{0.5},

## 2. Experiments

## 3. Results

#### 3.1. τ(med) Estimation for Different Latitudes

#### 3.2. TEC Variations

#### 3.3. foF2 Variations

#### 3.3.1. foF2 Reconstruction Validation

_{2}(Figure 9). O/N

_{2}was measured by the Global UltraViolet Imager (GUVI) at TIMED spacecraft. The role of this ratio was emphasized in different works (for example, in References [22,45] and references therein).

_{2}at F region heights results in the decrease of electron concentration [45]. During geomagnetic storms, the O/N

_{2}-associated negative phase of ionospheric disturbance can expand from the high-latitudes equatorward, which was the case with storm №5. Figure 9 proves the thermospheric ratio decrease during this geomagnetic storm.

#### 3.3.2. Latitudinal foF2 Variations

## 4. Discussion

#### 4.1. foF2 Response to the Storms during 7–17 March 2012

#### 4.2. foF2 Response to the Storm during 21–31 March 2012

- (1)
- The ionospheric responses to MP and RP of geomagnetic storms differed. The change in the ionospheric reaction was quite clear in four cases.
- (2)
- The ionosphere responded to the MP of each storm 2 h after its beginning (later in one case). It also changed its behavior ~2 h after the storm’s RP beginning in four cases (Figure 12a,d).
- (3)
- The ionosphere returned to its regular state rather quickly after each geomagnetic storm. Therefore, though the short period of 7–17 March was characterized by a series of geomagnetic disturbances, it was possible to distinguish the response to each particular storm.
- (4)
- The ionospheric structures such as MIT and the border of the northern crest of EIA were more prominent during all storms (higher electron density gradients) instead of being smoothed and sometimes shifted as on non-storm days. Sometimes they manifested themselves in much sharper forms and/or were shifted in latitude if compared to their quiet regular patterns. For instance, foF2 curves in Figure 12b,c,e,f.
- (5)
- The response to storm №5 developed at an already non-quiet ionospheric background: foF2 values were increased under quiet geomagnetic conditions most of the time especially at high latitudes. During the storm, the foF2 values were exactly the opposite to these background variations: decreased at high latitudes instead of being increased and increased more intensively than during geomagnetically quiet days at lower latitudes. Eventually, this confirms the preliminary conclusion indicating that the ionospheric behavior was probably controlled by O/N
_{2}changes along the 70° W longitude due to geomagnetic storm impact.

## 5. Correlation between the Ionospheric and Space Weather Parameters

#### 5.1. Paired Correlation Analysis

#### 5.2. Multiple Correlation Analysis

- (a)
- In our case, ∆foF2(rec) was considered as a “dependent” parameter (response variable) which was influenced by a set of SW parameters variations (explanatory variables). Considering the solar wind and interplanetary environment triggers of each geomagnetic storm discussed in Section 2 (Figure 2), we selected IMF, Bz, Np, V and AE to be included into the set of explanatory variables. F10.7-index was not involved as it characterizes the longer-term variations of solar activity than the considered 11-day periods. Dst-index was not involved because we already included AE; and Dst and AE variations were very similar which preferably should be avoided for explanatory variables in PCA. Thermospheric ratio O/N
_{2}played a significant role in the ionospheric behavior (see Section 3). Consequently, it was included in the explanatory variables set, but only for the analysis at high and mid latitudes. This is because the ratio almost did not change at low latitudes and there were too many gaps of GUVI/TIMED satellite data at very high latitudes. - (b)
- Further, the data were standardized, which means transformation of data distribution into the new distribution with zero mean and single (unitary) standard deviation. This results in that all explanatory variables have the same statistical weight in order to highlight the variance contrast.
- (c)
- Then, the principal components (PCs) were calculated for this new dataset. Each PC is a linear combination of the uncorrelated original explanatory variables, which forms an eigenvector of the covariance–correlation matrix. The response variable can be expressed via PCs as follows:∆foF2 = a × PC1 + b × PC2 + c × PC3 + d × PC4 + e × PC5 (+ f × PC6),PC1 = L
_{11}× AE + L_{12}× V + L_{13}× Np + L_{14}× Bz + L_{15}× IMF (+ L_{16}× O/N_{2}),_{ij}are the loadings of PCi in terms of the original explanatory variables (IMF, Bz, Np, V and AE), or in other words, the correlation coefficients between IMF, Bz, Np, V, AE and PCs. Figure 15b shows the example of the covariance matrix containing the loadings for time series of ∆foF2 during 7–17 March 2012: Each column represents the loadings for a particular PC. - (d)
- The scree plot is a graph that shows the magnitudes of the eigenvalues of the covariance–correlation matrix. For example, Figure 15c illustrates the level of each PC impact on the response variable (percentage of ∆foF2 variance explained by a particular PC). Usually, it is supposed that it is sufficient to consider the components that explain 85% of the response variable variations; and the components of minor influence may be neglected. Though three first PCs mostly explained more than 85% of ∆foF2 variations, we considered five components. This is because in our case the same original explanatory variable could contribute significantly to several PCs (for instance, IMF in PC1, PC3 and PC4 in Figure 15b) [50]. The analysis showed that the consideration of less than five components resulted in the false intensification or decrease of the role of such explanatory variables.
- (e)
- Formulae 5 and 6 describe the PCA decomposition and a consequent regression step represented by PCR. Preferably, the explanatory variables should be totally independent from each other. From the physical point of view, in our case they are not absolutely independent because eventually they represent different processes that define Space Weather conditions. That is why, the direct comparison of IMF, Bz, Np, V and AE contributions to PCs (values of their loadings in each column of the matrix) resulted in the confusing results meaning that PCA was not sufficient to draw the conclusions. To eliminate the multicollinearity between our explanatory variables, PCR [51] was performed which is basically an extension of PCA. In PCR analysis, instead of regression of the dependent ∆foF2(rec) on the explanatory variables directly, the principal components or eigenvectors (v) of their variance–covariance matrix coefficients of explanatory variables (Figure 15b) are used as regressors (Equation (6)). Typically, only a subset of all the principal components is used for regression, making PCR a kind of regularized procedure or shrinkage estimator. According to equation 6, the final regression coefficients were obtained by multiplying PC values calculated for ∆foF2(rec) by the corresponding loading values (Figure 15d). ∆foF2(rec) of the particular latitude and time delay from the storm beginning were analyzed separately.
- (f)
- Finally, the contribution of variations of each SW parameter on the ionospheric response was presented in the form of percentage of the “explained” variance of ∆foF2(rec), based on the regression coefficient values obtained in PCR. Considering the contribution of each parameter to a particular PC, the dominant contributions or, in other words, the factors that had a dominant influence on foF2 at the particular latitude can be qualitatively estimated.

_{2}during 11 days and the corresponding day-to-day variation of foF2(rec) value at a particular UT hour. The daily averaged SW parameters values characterize the overall level of SW perturbation during the particular day.

#### 5.2.1. 7–17 March 2012

_{2}variations became clear. It was most pronounced at mid latitudes. It is logical because the main changes of the thermospheric composition during geomagnetic storms occurred near this latitude in the considered sector. At mid latitudes, O/N

_{2}impact was observed at all hours, being the lowest at the evening and the highest under the daytime conditions. At high latitudes, O/N

_{2}played a leading role during the daytime with a tendency of slight decrease in the evening.

#### 5.2.2. 21–31 March 2012

_{2}was delayed. It may seem surprising that the O/N

_{2}role is less emphasized during the analyzed period than it seemed from observations discussed in Section 3. This is because 21–31 March included only two storm days; and, in general, under quiet geomagnetic conditions, O/N

_{2}variations did not have such impact on foF2 as during the storm.

_{2}variations in the considered latitudinal sector during geomagnetic disturbances would lead to incorrect conclusions.

## 6. Conclusions

- Latitudinal dependence of the median value of the ionospheric slab thickness was obtained with use of polynomial approximation. The polynomial of third degree provided the confidence factor close to 1 for all UT hours except 12 UT (~7 LT), when the linear approximation with the confidence factor of 0.98 was sufficient.
- The synchronicity of changes of experimental TEC and foF2 values (changes of their behavior) was shown by data of four ionosondes during disturbances.
- The suggested method of construction of τ(med) latitudinal dependence applied to the analysis of foF2 during the disturbances of March 2012 allowed us to reveal the latitudinal features, which generally confirm the results of studies of such variations performed for local regions or for separated magnetic storms. In particular, (a) MIT structure and the border of the EIA northern crest manifested themselves in the much sharper and prominent forms and/or were shifted in latitude during all storms (higher electron density gradients). (b) Ionospheric response was delayed by 2 h from the storm’s beginning, in most cases (by 5–6 h in one case). The responses to the main and recovery phases in most cases was different. (c) The response to the storm of 27–28 March developed at an already non-quiet ionospheric background and was controlled by O/N
_{2}changes due to geomagnetic storm impact. - A qualitative assessment of the differences in the degree of influence of SW parameters variations on the ionosphere of different latitudes for two periods was obtained. The results of multiple correlation analysis for 7–17 March and 21–31 March differed significantly, but in both cases, during the geomagnetic disturbances, O/N
_{2}variations in the considered longitudinal sector played a significant role in the ionospheric state change at mid latitudes. During the first period, the solar wind speed played the dominant role at high and very high latitudes. At high, mid and low latitudes, the impacts of several phenomena were difficult to separate. This combination of impacts depended on day/night conditions. During the second period, the geomagnetic storm developed on the quiet geomagnetic background, and the role of geomagnetic field changes was dominant.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Space Weather parameter variations during 7–17 March and 25–29 March, 2012: (

**a**) F10.7 index, (

**b**) averaged magnitude of Interplanetary Magnetic Field (IMF), (

**c**) proton density, (

**d**) Bz-component of IMF, (

**e**) solar wind proton temperature, (

**f**) solar wind speed, (

**g**) Dst-index, (

**h**) AE-index and (

**i**) Kp-index. Storm events are numbered 1–5.

**Figure 3.**Diurnal variation of (

**a**) experimental medians of τ for four ionosonde stations, (

**b**) τ medians for three arbitrary latitudes according to the polynomial approximation and (

**c**) latitudinal distribution of the equivalent slab thickness at different hours of the day.

**Figure 4.**Total Electron Content (TEC) (left panels) and reconstructed foF2 (right panels) variations along the meridian of 70° W: (

**a**,

**b**) monthly median values; (

**c**,

**d**) during MP and RP on 7 March; (

**e**,

**f**) before and during MP on 15 March.

**Figure 5.**Latitudinal TEC dependences during 7–17 March 2012 for local: (

**a**) evening, (

**b**) night, (

**c**) morning and (

**d**) day hours.

**Figure 6.**The same as in Figure 5 but during 21–31 March 2012.

**Figure 7.**Parameter variations during 6–17 March 2012 at Millstone Hill station (left panels) and Thule station (right panels): (

**a**,

**b**) observed and median TEC values; (

**c**,

**d**) observed, median and reconstructed foF2 values; and (

**e**,

**f**) δTEC, δfoF2 and 0.5Dst variations.

**Figure 8.**The same as in Figure 7 but during 21–31 March 2012 at Sondrestrom station (

**left panels**); Puerto Rico station (

**right panels**).

**Figure 9.**Thermospheric O/N

_{2}ratio during (

**a**) 26 March (quiet day), (

**b**) 27 March (partially MP of the storm) and (

**c**) 28 March (partially RP of the storm).

**Figure 10.**The same as in Figure 5 but for latitudinal foF2(rec) dependences.

**Figure 11.**The same as in Figure 10 but during 21–31 March 2012.

**Figure 12.**Examples of foF2 latitudinal dependence during quiet periods (blue curves) and during disturbances (emerald curves with rectangles): (

**a**) 7 March (MP beginning), (

**b**) 7 March (developed MP), (

**c**) 7 March (developed RP), (

**d**) 15 March (MP beginning), (

**e**) 7 March (Dst minimum) and (

**f**) 16 March (after RP).

**Figure 13.**foF2 latitudinal dependence during 21–31 March: (

**upper panels**) typical examples during quiet geomagnetic conditions (control days); (

**lower panels**) variations at the same hours but during the storm. Curves designations are the same as in Figure 12.

**Figure 14.**Examples of correlations between foF2(rec) and Space Weather (SW) parameters at the particular hours. Orange curve stands for 7–17 March, and green curve for 21–31 March.

**Figure 15.**The results of Principal Components Analysis (PCA) for ∆foF2 time series at 77.5° N during 7–17 March 2012: (

**a**) distribution of ∆foF2 values (vectors in the planes of five original explanatory variables) as a function of principal components PC1 and PC2; (

**b**) covariance matrix; (

**c**) scree plot of PC impacts; (

**d**) multiple regression coefficients of the response variable in terms of PCs.

Storm № | MP Beginning | RP Beginning | Minimum Dst Value | Maximum Kp Value |
---|---|---|---|---|

1 | 7 March ~04 UT | 7 March ~09 UT | −88 nT | 6 |

2 | 9 March ~01 UT | 9 March ~08 UT | −145 nT | 8 |

3 | 12 March ~10 UT | 12 March ~16 UT | −64 nT | 6 |

4 | 15 March ~14 UT | 15 March ~20 UT | −88 nT | 6 |

5 | 27 March ~10 UT | 28 March ~04 UT | −68 nT | 5 |

**Table 2.**Main contributors to foF2(rec) at high latitudes (HL), mid latitudes (ML) and low latitudes (LL), along 70° W.

Ionospheric Response Delay | HL: 77.5° N | HL: 67.5° N | ML: 42.5° N | LL: 17.5° N |
---|---|---|---|---|

(87.2° N) | (77.2° N) | (52.2° N) | (27.3° N) | |

0 h | V(40%) | V(35%) | IMF(37%) | AE(43%) |

Np(23%) | IMF(26%) | V(25%) | Bz(28%) | |

AE(20%) | Np(23%) | AE(22%) | IMF(19%) | |

2 h | Bz(30%)V(27%) Np(23%) | V(44%)AE(19%) Np(18%) | IMF(49%)V(28%) Bz(21%) | AE(53%) |

IMF(18%) | ||||

Bz(15%) | ||||

Np(14%) | ||||

4 h | V(54%)Bz(29%) | V(42%) | AE(39%)Bz(30%) | AE(64%) |

AE(30%) | IMF(17%) | |||

IMF(13%) | V(17%) |

Hour | HL: 77.5° N | HL: 67.5° N | ML: 42.5° N | LL: 17.5° N |
---|---|---|---|---|

(87.2° N) | (77.2° N) | (52.2° N) | (27.3° N) | |

0 UT (~19 LT) | Np(38) IMF(34) | Np(35) V(32) IMF(30) | IMF(36) Bz(36) Np(20) | V(26)Np(23)Bz(22)AE(21) |

Np(30)V(27)IMF(23)O/N_{2}(16) ^{1} | IMF(37) Bz(32) O/N_{2}(16) ^{1} | |||

6 UT (~1 LT) | IMF(35) V(25) | IMF(43) Np(31) V(19) | Np(34) Bz(32) | IMF(40)AE(32)V(20) |

IMF(39) Np(32) V(23) ^{1} | Np(31) Bz(30) O/N_{2}(26) ^{1} | |||

12 UT (~7 LT) | Bz(33)AE(28)V(28) | Bz(36) IMF(21) | Np(28)AE(23)V(23)IMF(19) | IMF(37)Np(34) |

Bz(34) IMF(22) ^{1} | Np(28) O/N(28) _{2}^{1} | |||

18 UT (~13 LT) | Bz(33)Np(28)V(24) | Np(27) V(27) | Bz(41) IMF(30) AE(22) | Np(26)AE(24) V(22) |

O/N(40) AE(35) _{2}^{1} | O/N(39) AE(28) _{2}^{1} |

^{1}Variables include O/N

_{2}.

**Table 4.**The same as in Table 2 but for 21–31 March 2012.

Ionospheric Response Delay | HL: 77.5° N | HL: 67.5° N | ML: 42.5° N | LL: 17.5° N |
---|---|---|---|---|

(87.2° N) | (77.2° N) | (52.2° N) | (27.3° N) | |

0 h | Bz(54%) V(27%) | Bz(27%) IMF(26%)V(23%)AE(16%) | IMF(50%) V(26%) Np(18%) | AE(36%)Bz(23%) |

2 h | AE(52%) V(30%) | AE(35%) IMF(27%) V(26%) | V(38%) IMF(34%) | AE(42%) V(32%) |

4 h | AE(55%) | AE(37%) V(26%) IMF(24%) | V(29%) Bz(21%) IMF(20%) | AE(36%) V(31%) |

**Table 5.**The same as in Table 3 but for 21–31 March 2012.

Hour | HL: 77.5° N | HL: 67.5° N | ML: 42.5° N | LL: 17.5° N |
---|---|---|---|---|

(87.2° N) | (77.2° N) | (52.2° N) | (27.3° N) | |

0 UT (~19 LT) | Bz(44) AE(31) | IMF(39) AE(22) Bz(19) | AE(34) IMF(32) Bz(20) | AE(44) Bz(26) |

AE(33) Bz(27) ^{1} | AE(39) Bz(26) ^{1} | |||

6 UT (~1 LT) | AE(37) Np(30) | AE(42) Bz(24) IMF(21) | AE(42) Bz(26) IMF(24) | AE(38) Np(32) |

AE(43) Bz(26) IMF(20) ^{1} | AE(41) Bz(27) ^{1} | |||

12 UT (~7 LT) | AE(35) Bz(35) IMF(21) | AE(46) IMF(19) Bz(18) | AE(45) Bz(20) IMF(18) | Np(32)IMF(25)Bz(24) |

AE(31) Bz(31) ^{1} | AE(45) Bz(20) ^{1} | |||

18 UT (~13 LT) | Bz(49)Np(18)AE(16)IMF(16) | AE(63) | AE(42) Bz(25) | Bz(32)AE(30)IMF(19) |

AE(63) ^{1} | O/N(28)_{2}Np(26)AE(22) ^{1} |

^{1}Variables include O/N

_{2}.

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**MDPI and ACS Style**

Sergeeva, M.A.; Maltseva, O.A.; Caraballo, R.; Gonzalez-Esparza, J.A.; Corona-Romero, P.
Latitudinal Dependence of the Ionospheric Slab Thickness for Estimation of Ionospheric Response to Geomagnetic Storms. *Atmosphere* **2021**, *12*, 164.
https://doi.org/10.3390/atmos12020164

**AMA Style**

Sergeeva MA, Maltseva OA, Caraballo R, Gonzalez-Esparza JA, Corona-Romero P.
Latitudinal Dependence of the Ionospheric Slab Thickness for Estimation of Ionospheric Response to Geomagnetic Storms. *Atmosphere*. 2021; 12(2):164.
https://doi.org/10.3390/atmos12020164

**Chicago/Turabian Style**

Sergeeva, Maria A., Olga A. Maltseva, Ramon Caraballo, Juan Americo Gonzalez-Esparza, and Pedro Corona-Romero.
2021. "Latitudinal Dependence of the Ionospheric Slab Thickness for Estimation of Ionospheric Response to Geomagnetic Storms" *Atmosphere* 12, no. 2: 164.
https://doi.org/10.3390/atmos12020164