Research on the Automatic Calculation Method of Relative Sunspot Number Based on SDO/HMI White Light Images

doi:10.11871/jfdc.issn.2096-742X.2026.02.008

Abstract

Abstract:

[Objective] To automatically calculate the relative sunspot number by using the high-resolution white light image captured by the Solar Dynamics Observatory (SDO). [Methods] Firstly, a segmentation algorithm with double grayscale thresholds is used to achieve the accurate segmentation of the umbra-penumbra structure of sunspots, so as to calculate the number of sunspots Ns. Subsequently, the density-based DBSCAN clustering algorithm is employed to cluster the segmented sunspots to obtain the number of sunspot groups Ng. Then, based on Ns and Ng obtained from the previous steps, the calculation results are fitted with the relative sunspot numbers released by the Solar Influences Data Analysis Center through the least squares method to determine the optimal personal observation coefficient k. Finally, the values are substituted into the formula to obtain the relative sunspot number R. [Results] The correlation coefficients between the calculated results of relative sunspot numbers in 2014 and 2017 and the data from the Solar Influences Data Analysis Center are 0.913 and 0.960, respectively, with RMSE values of 16.76 and 6.07, respectively. [Limitations] The performance of the algorithm varies during different solar activity periods (solar maximum and solar minimum), leading to significant fluctuations in individual observation coefficient k-values. Consequently, dynamic k-values tailored to different solar activity levels may need to be implemented in the future. [Conclusions] The algorithm proposed in this paper realizes the automatic calculation of the relative sunspot number, which greatly alleviates the problem that the traditional manual calculation of the relative sunspot number relies on expert experience. It is expected to replace manual work and realize the automatic calculation of the relative sunspot number.

Key words: Sunspot, relative sunspot number, thresholding method, SDO/HMI

ZHAO Xingkai, ZOU Ziming, LI Yunlong. Research on the Automatic Calculation Method of Relative Sunspot Number Based on SDO/HMI White Light Images[J]. Frontiers of Data and Computing, 2026, 8(2): 98-110, https://cstr.cn/32002.14.jfdc.CN10-1649/TP.2026.02.008.

Figures/Tables 14

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Table 1

Table 2

Fig.9

Fig.10

Fig.11

Fig.12

References 27

[1]	USOSKIN I. A history of solar activity over millennia[J]. LIVING REVIEWS IN SOLAR PHYSICS, 2017, 14(1): 3. DOI: 10.1007/s41116-017-0006-9.
[2]	CLETTE F, SVALGAARD L, VAQUERO J M, et al. Revisiting the Sunspot Number A 400-Year Perspective on the Solar Cycle[J]. Space Science Reviews, 2014, 186(1-4): 35-103. DOI:10.1007/s11214-014-0074-2.
[3]	VANLOMMEL P, CUGNON P, LINDEN R A M V D, et al. The Sidc: World Data Center for the Sunspot Index[J]. Solar Physics, 2004, 224(1-2): 113-120. DOI: 10.1007/s11207-005-6504-2.
[4]	CLETTE F, LEFÈVRE L. The New Sunspot Number: Assembling All Corrections[J]. Solar Physics, 2016, 291(9-10): 2629-2651. DOI:10.1007/s11207-016-1014-y.
[5]	VAQUERO J M. Historical sunspot observations: A review[J]. Advances in Space Research, 2007, 40(7): 929-941. DOI:10.1016/j.asr.2007.01.087.
[6]	CORTESI S, CAGNOTTI M, BIANDA M, et al. Sunspot Observations and Counting at Specola Solare Ticinese in Locarno Since 1957[J]. Solar Physics, 2016, 291(9-10):3075-3080.DOI:10.1007/s11207-016-0872-7.
[7]	ZHARKOV S, ZHARKOVA V, IPSON S, et al. Technique for automated recognition of sunspots on full-disk solar images[J]. EURASIP Journal on Advances in Signal Processing, 2005, 15: 2573-2584. DOI: 10.1155/ASP.2005.2573.
[8]	CURTO J J, BLANCA M, MARTÍNEZ E. Automatic Sunspots Detection on Full-Disk Solar Images using Mathematical Morphology[J]. Solar Physics, 2008, 250(2): 411-429. DOI: 10.1007/s11207-008-9224-6.
[9]	ZHAO C, LIN G, DENG Y, et al. Automatic Recognition of Sunspots in HSOS Full-Disk Solar Images[J]. Publications of the Astronomical Society of Australia, 2016, 33: e018. DOI: 10.1017/pasa.2016.17.
[10]	COLAK T, QAHWAJI R. Automated McIntosh-Based classification of sunspot groups using MDI images[J]. Solar Physics, 2008, 248(2): 277-296. DOI:10.1007/s11207-007-9094-3.
[11]	李泠, 崔延美, 刘四清, 等. 太阳黑子自动识别与特征参量自动提取[J]. 空间科学学报, 2020, 40(3): 315-322.
[12]	ZHAO C, YANG S, WANG T, et al. An Automatic Approach for Grouping Sunspots and Calculating Relative Sunspot Number on SDO/HMI Continuum Images[J]. The Astronomical Journal, 2024, 167(2): 52. DOI: 10.3847/1538-3881/ad11e2.
[13]	BOURGEOIS S, BARATA T, ERDÉLYI R, et al. Sunspots Identification Through Mathematical Morphology[J]. Solar Physics, 2024, 299(2): 10. DOI: 10.1007/s11207-023-02243-1.
[14]	MOURATO A, FARIA J, VENTURA R. Automatic sunspot detection through semantic and instance segmentation approaches[J]. Engineering Applications of Artificial Intelligence, 2024, 129: 107636. DOI:10.1016/j.engappai.2023.107636.
[15]	FAN D, YANG Y, FENG S, et al. SIPNet & SAHI: Multiscale Sunspot Extraction for High-Resolution Full Solar Images[J]. Applied Sciences, 2023, 14(1): 7. DOI: 10.3390/app14010007.
[16]	SANTOS J, PEIXINHO N, BARATA T, et al. Sunspot Detection Using YOLOv5 in Spectroheliograph H-Alpha Images[J]. Applied Sciences, 2023, 13(10): 5833. DOI: 10.3390/app13105833.
[17]	赵梓良, 刘家真, 胡真, 等. 一种层次化的太阳黑子快速自动识别方法[J]. 光电工程, 2020, 47(7): 39-49.
[18]	PALLADINO L, NTAGIOU E, KLUG J, et al. Sunspot Groups Detection and Classification on SDO/HMI Images using Deep Learning Techniques[C]// 2022 IEEE Aerospace Conference (AERO). New York: IEEE, 2022: 1-10. https://ieeexplore.ieee.org/document/9843222/. DOI: 10.1109/AERO53065.2022.9843222.
[19]	FINI. A deep learning approach to sunspot detection and counting[D]. Politecnico di Milano, 2019. https://www.politesi.polimi.it/handle/10589/147435.
[20]	DASGUPTA U, SINGH S, JEWALIKAR V. Sunspot Number Calculation Using Clustering[C]// 2011 Third National Conference on Computer Vision, Pattern Recognition, Image Processing and Graphics, 2011: 171-174. https://ieeexplore.ieee.org/document/6133028/. DOI: 10.1109/NCVPRIPG.2011.43.
[21]	Which time tag should be attached to each daily International Sunspot Number? \| SIDC[EB]. https://www.sidc.be/SILSO/faq8.
[22]	LIN G H, WANG X F, LIU S, et al. Chinese Sunspot Drawings and Their Digitization -(I) Parameter Archives[J]. Solar Physics, 2019, 294(6): 79. DOI: 10.1007/s11207-019-1456-0.
[23]	BARANYI T, GYORI L, LUDMANY A, et al. Comparison of sunspot area data bases[J]. Monthly Notices of the Royal Astronomical Society, 2001, 323(1): 223-230. DOI: 10.1046/j.1365-8711.2001.04195.x.
[24]	BERGHMANS D, CLETTE F, CUGNON P, et al. The solar influences data analysis centre[J]. Journal of Atmospheric and Solar-Terrestrial Physics, 2002, 64(5-6): 757-761. DOI: 10.1016/S1364-6826(02)00037-8.
[25]	AYDIN B, ANGRYK R. Spatiotemporal Frequent Pattern Mining on Solar Data:Current Algorithms and Future Directions[C]// 2015 IEEE International Conference on Data Mining Workshop (ICDMW). Atlantic City, NJ, USA: IEEE, 2015: 575-581. http://ieeexplore.ieee.org/document/7395719/. DOI: 10.1109/ICDMW.2015.10.
[26]	OTSU N. Threshold Selection Method from Gray-Level Histograms[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1979, 9(1): 62-66. DOI: 10.1109/TSMC.1979.4310076.
[27]	DUAN L, XU L, GUO F, et al. A local-density based spatial clustering algorithm with noise[J]. Information Systems, 2007, 32(7): 978-986. DOI: 10.1016/j.is.2006.10.006.

Eps	70	80	90
MinPts
15	3.36	2.89	2.59
20	2.65	2.3	2.05
25	2.18	1.92	1.72

Eps	85	95	100
MinPts
25	1.82	1.69	1.65
30	1.61	1.56	1.56
35	1.56	1.55	1.58