# The Contribution of Large Recurrent Sunspot Groups to Solar Activity: Empirical Evidence

## Abstract

**:**

## 1. Introduction

## 2. Data

## 3. Method

#### 3.1. Focus of the Identification

#### 3.2. Identification of the Recurrent Groups

#### 3.3. Samples of Large and Moderate Nestles

## 4. Results

#### 4.1. Indices of Recurrent Sunspot Groups

#### 4.2. Recurrent Sunspot Group Lifetime

## 5. Discussion

## 6. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Rules Applied to Define Recurrent Sunspot Groups

**Rule**

**1.**

**Rule**

**1′.**

**Rule**

**2.**

**Rule**

**3.**

**Rule**

**4.**

## Appendix B. Choice of the Ellipse Semi-Axes

**Figure A1.**Training: The ${F}_{1}$ score calculated on sunspot groups from the training set ${\Omega}_{A,T}$ with the low threshold A of the maximal area, the variable time gap T between the observations and the longitudinal and latitudinal semi-axes of the ellipse ${l}_{x}$ and ${l}_{y}$, respectively. Upper row is corresponding to $A=950$, lower – to $A=0$.

**Table A1.**The number of the type I and II errors for large ($A>950$ MH) and moderate ($A>700$ MH) recurrent groups; $T=10$.

$\mathit{A}>950$ MH | Ellipse Size ${12}^{\circ}\times {2}^{\circ}$ | Ellipse Size ${12}^{\circ}\times {5}^{\circ}$ | Number of the Groupsin the Training Set |
---|---|---|---|

Error type I ($fp$) | 14 | 8 | 529 |

Error type II ($fn$) | 148 | 27 | |

$A>700$ MH | ${12}^{\circ}\times {2}^{\circ}$ | ${12}^{\circ}\times {5}^{\circ}$ | Number of the groupsin the training set |

Error type I ($fp$) | 26 | 22 | 920 |

Error type II ($fn$) | 238 | 43 |

**Table A2.**The errors in the identification of large sunspot groups with the ellipses of the sizes ${12}^{\circ}\times {2}^{\circ}$ (roughly corresponding to [7]) and ${12}^{\circ}\times {5}^{\circ}$ used in this paper on the training set (A3) defined with the 1944–1976 RGO/SOON catalogues and $T=10$. The RGO/SOON ID are given; the pairs of the ID show the two groups that are erroneously united into a single group.

$\mathit{A}>950$ MH | ${12}^{\circ}\times {2}^{\circ}$ | ${12}^{\circ}\times {5}^{\circ}$ |
---|---|---|

Error type I | (18872, 18882), | (19061, 19062), |

(18959, 18971) | ||

Error type II | 18559, 21356, 19200, 21506 | 17782, 18756 |

14838, 16486, 18756, 20125, 23119 | ||

14717, 15638, 17161, 17782 |

## Appendix C. Comparison with Other Identifications

- (1)
- The matching of the groups with ID 4285–4296 presented in RGO and GPR(linked) is also with our catalogue $\mathbf{L}$;
- (2)
- 4369–4386 is presented in GPR(linked) and $\mathbf{M}$;
- (3)
- 4376–4399 presented in RGO and $\mathbf{M}$ is replaced by the matching 4376–4395 in GPR(linked);
- (4)
- 4416–4435–4448 in GPR(linked) corresponding to 4416–4435–4446 in RGO is identified as 4435–4447 in $\mathbf{M}$ (Rule 4 violated);
- (5)
- 4428–4441 is presented in GPR(linked) and $\mathbf{L}$;
- (6)
- 4456–4473 is presented in RGO, GPR(linked), and $\mathbf{M}$ (note that GPR(linked) contains the matching 4457–4473 in addition).

## Appendix D. Example of Potentially Wrong Identification

**Figure A2.**The movement of the sunspot group 11263–11277/11279 (recorded from 29 July 2011 till 4 September 2011) supposed to be recurrent. Data are freely downloaded from SolarMonitor.org (accessed on 5 January 2022).

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**Figure 1.**The 11-year moving averages ${R}_{\mathrm{ISSN}}$, ${R}_{D}$, ${R}_{M}$, and ${R}_{L}$ of index ISSN and the areas of all, medium, and large selected sunspots, respectively, in line with (1); ${R}_{\mathrm{ISSN}}$ and ${R}_{D}$ are scaled to fit the Y-range.

**Figure 2.**The normalized composites ${r}_{M}={R}_{M}/{R}_{D}$ and ${r}_{L}={R}_{L}/{R}_{D}$ of the areas of the moderate and large selected sunspot groups; specific normalization ${r}_{L,1.35}^{*}\sim {R}_{L}/{R}_{D}^{1.35}$ and the composite ${R}_{D}$ of the areas of the all sunspots (both rescaled by an appropriate constant ${C}_{L}$ and number $1/3200$, respectively).

**Figure 3.**The composites ${r}_{H,\beta}^{*}$ (black), ${r}_{LH,\beta}^{*}$ (gray), ${r}_{L,\beta}^{*}$ (magenta) obtained through the normalization (2) with a power function ${r}_{D}^{\beta}$ of the activity, where $\beta $ equalled to $1.20$, $1.19$, and $1.35$, respectively, is adjusted to each composite separately. Scaled solar activity given with the index ${R}_{G}$ (red) and the boundaries of the solar cycles (vertical lines) are for illustrative purposes.

**Figure 4.**The 22-year moving averages ${\tau}_{{D}^{\u2033}}$ (in blue), ${\tau}_{L}$ (in magenta), and ${\tau}_{M}$ (in yellow) of the lifetime per day calculated for the groups from the catalogues ${\mathbf{D}}^{\u2033}$, $\mathbf{L}$, and $\mathbf{M}$ representing large recurrent sunspot groups, moderate recurrent sunspot groups and all groups recorded after the identification and related to that examined in [19]. Daily ISSN (scaled) is in black.

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Shapoval, A.
The Contribution of Large Recurrent Sunspot Groups to Solar Activity: Empirical Evidence. *Universe* **2022**, *8*, 180.
https://doi.org/10.3390/universe8030180

**AMA Style**

Shapoval A.
The Contribution of Large Recurrent Sunspot Groups to Solar Activity: Empirical Evidence. *Universe*. 2022; 8(3):180.
https://doi.org/10.3390/universe8030180

**Chicago/Turabian Style**

Shapoval, Alexander.
2022. "The Contribution of Large Recurrent Sunspot Groups to Solar Activity: Empirical Evidence" *Universe* 8, no. 3: 180.
https://doi.org/10.3390/universe8030180