筑波学院大学紀要第18集

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2023年＜研究ノート＞

A proposal for
Clustering of Sunspots using Machine Learning to
Explore Inter-cycle Patterns
Bhola PANTA ＊Abstract
Sunspots were first observed by telescope in 1610. This makes a record of more than 400years. Even with a long history and abundance of ground-based and space borne observatory data,
fundamental questions about their formation are still shrouded in mystery. Hence, sunspots are oneof the most studied phenomena in solar physics. The research on sunspots is important because
they are precursors to solar flares, which can have profound impact on life here on earth. We propose a machine learning based clustering technique of the sunspot time series data to find sunspot
patterns between solar cycles. This will eventually be correlated with solar flare data to understandthe patterns of solar flare occurrences in future sunspot cycles. Ultimately, we expect to contributeto develop a more efficient space weather forecasting system. This research note presents a preliminary investigation of the issue in question, and a roadmap.
Key words: Sunspots, Solar flare, Machine learning, Clustering, Particle Swarm Optimization

1. Introduction
Every once in a while, we all see news about “solar flares” on TV and other news outlets. A solar
flare is a large-scale explosion that occurs around a sunspot on the “surface” of the sun, called thephotosphere. High-energy particles and radiation from the flare travel to the Earth. Depending on
the scale of the flare, it can cause various damages. Induced currents can enter power lines andaffect the power grid, communication satellites can break down or stop functioning, etc. Researchon “space weather” caused by such phenomena is an active research field around the world. In theUSA, National Oceanic and Atmospheric Administration (NOAA)ʼs Space Weather Prediction Center(SWPC) continually monitors and forecasts Earthʼs space environment, providing solar-terrestrial
information. In Japan, the National Institute of Information and Communications Technology (NICT)
provides space weather forecasts.
Sunspots are temporary spots on the photosphere. These spots are formed and grow in size,as they move across the disk of the sun. They eventually decay. Individual sunspots or groups ofsunspots may have a lifespan of several days to a few months. Solar flares and other temporary＊

筑波学院大学 経営情報学部、Tsukuba Gakuin University─ 115 ─

筑波学院大学紀要182023

events like coronal mass ejection (CME) mostly occur around sunspots. George Ellery Hale (18681938) discovered magnetic fields in sunspots. The sunspots appear in the magnetically activeregions. The strong magnetic flux on the sunspots hinders convection from the inner core of thesun, resulting in reduced temperature, which in turn makes the spots appear darker than thesurrounding areas.
In the past 100 years, we have seen notable developments in instrumentation to carr y out
observation, better understanding of polarized light (for spectroscopic analysis) and better modelingcapabilities (e.g., MHD) to work on the theoretical aspects [10]. Thanks to those developments, we
now have plenty of data of high accuracy, resolution and cadence, specially from the space-borne
observatories like the well-known Solar Dynamics Observatory (SDO) and Solar and Heliospheric
Observatory (SOHO). With such developments, solar astronomy has stepped in “big data”, in which
tools and techniques of data science are expected to play a significant role in the near future, tofurther unravel the mysteries of the sun.

2. Motivation
As mentioned earlier, abundance of observation data from ground based as well as space-borne
observatories are available. This has created huge challenges in terms of transferring data fromthe observation site to the storage site, processing “raw data” to produce “science-ready data” andstoring. At the same time, with significant increase in computing power, including the availability ofGPUs, it is becoming increasingly possible to apply machine learning techniques to reduce humanlabor when processing huge volumes of data. For example, in the case of the solar radio observation
data, it is said that less than 5% of the data is valuable to solar physicists [13]. Hence the importanceof machine learning-enabled classification algorithms cannot be overstated: even a binary (useful/not useful) classifier would dramatically free up astronomers to do more productive tasks.
Using data science techniques, we would like to explore if there is any hidden pattern insunspotʼs appearance over a sunspot cycle. Starting from the sunspotʼs distribution in time (dateof appearance) and space (where they appear on the sunʼs disk) for each sunspot-cycle, we will tryto analyze if there is any pattern that may be applied to another cycle. Together with the solar flare
database from various observatories and analyzing the sunspot data at the flare date and time, thesefindings may eventually be used to develop a more efficient space weather forecasting system.
Take for example, the X9-class solar flare of Dec. 5, 2006, shown in Fig. 1. (For flareclassification, readers are advised to reference appropriate literature. One example is [17]). The
source sunspot of the X9-class flare is shown in Fig.2. This research will try to analyze the sunspot
cluster data patterns, and analyze if correlations exist in other cycleʼs sunspots and flares.
Space weather forecasting is said to be several decades behind terrestrial weather forecasting.
We expect to evaluate the clustering models using various metrics (e.g., silhouette index, and Dunnindex) and propose efficient/reliable models. By feeding back the results to the data science andsolar research community, we hope to contribute to the space weather research and forecastingfield.

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Bhola PANTA：A proposal for Clustering of Sunspots using Machine Learning to Explore Inter-cycle Patterns

Fig. 1 The X9-class solar flare of Dec. 5,2006, observed by the Solar X-Ray
Imager aboard NOAA’s GOES-13
satellite. Credit: NOAA/SWPCFig. 2 S unspot 930, the source of thepowerful X9-flare on Dec. 5, 2006.
Credit: John Nassar

3. Related Works
Sunspots have been studied for a long time. According to Wikipedia, the earliest record ofsunspots is found in China, in a text composed before 800 BC [14]. After the invention of telescopes,
astronomers started to record observations more systematically. Since the sunʼs magnetic field
affects all aspects of solar activity [10], considerable literature exists analyzing sunspots andsolar flares in the light of magnetic fields, for example, either using MHD simulations or throughobserved data (magnetograms or radio observations).
Data-science based exploration of astronomy data in general and solar astronomy data inparticular are more recent phenomena. Since the third wave of the AI boom (2000-), we have seena huge increase in application of machine learning techniques in sunspot data analysis, especiallysince the introduction of deep learning in 2006 [5,9,13]. Mandal et al. [8] reviewed sunspot area
catalogs of nine archives, one of which is Debrecen Heliophysics Observatory archive. Stenninget al. [12] applied mathematical morphological analysis to extract numerical summaries of sunspot
images that can be used for automatic classification. de Toma et al. [6] analyzed changes in sunspotarea using photometric images over two solar cycles. Their findings were confirmed by USAF/NOAA and Debrecen data. This indicates our choice of Debrecen data is reliable. When necessary,
we will reference the above results.

4. Sunspot data
Debrecen Photoheliographic Data (DPD) [4,7] is a catalog of positions and areas of sunspots
compiled by using white-light full disc obser vations taken at Debrecen and Gyula Obser ving
Stations in Hungary, as well as at other observatories in Austria, Belgium, Egypt, Georgia, India,

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Italy, Japan, Russia, Spain, UK, Ukraine, USA and Uzbekistan. The DPD is published as an ASCII
file. A snapshot of the time series of the daily data is shown in Fig. 3.
For each spot, the following data are available: date of observation (year, month, day, hour, minuteand second, shown in column C1 of Fig.3), the origin of the obser vation (C2), the measured(projected) and the corrected areas of umbrae and the whole spot (C3 ~ C6), Julian date (C7),position angle of the northern extremity of the axis of rotation (measured eastward from the northpoint of the disk) (C8), and the heliographic latitude of the central point of the disk (C9). A detailed
description of the data is available at the DPD site. In our clustering proposal, we will use thenecessary columns, as described in the methodology section.

5. Methodology to be employed, and further Plan
In machine learning, clustering techniques are widely used to discover trends in a big dataset.
Clustering is an unsupervised machine learning technique for organizing data into groups. If there
are patterns in the sunspot data, an appropriate clustering technique may be able to identify when(temporal) and where (spatial) these patterns occur. For some popular clustering algorithms,
readers are advised to reference appropriate literature in data mining. One excellent reference is“Introduction to Data Mining”, by Tan, Seinbach, Karpatne and Kumar. (Pearson Publishing, 2018)

Fig. 3 A snapshot of the daily time-series data as provided by theDebrecen Heliophysics Observatory, from 1974 to 2016. To
ease data processing, the date column (C1) has been createdmerging individual columns for the year, month, day, hour,
minute and second, in the original dataset.

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Bhola PANTA：A proposal for Clustering of Sunspots using Machine Learning to Explore Inter-cycle Patterns

For each solar cycle, we will create 3-dimensional data clusters using (1) date of observation(column C1), (2) heliographic latitude of the central point of the disk on the observation (columnC9), and (3) daily sum of corrected whole spot area in millionths of the solar hemisphere (columnC6).
Since we are considering using daily time series data, we will use “Time Series Clustering”.
Since the DPD data has both temporal dimension (date of obser vation) and spatial dimension(heliographic latitude), we will perform both temporal as well as spatial clustering. Performanceof k-means clustering with the dynamic time warping (DTW) metric [16] will be evaluated. We will
also consider developing necessary algorithms to carry out the experiment when necessary.
In another implementation, a Particle Swarm Optimization (PSO) [1,2,3] based clustering will
be considered. Since PSO is an optimization algorithm, we need to cast the clustering problem as
an optimization problem. Eventually, we will consider a hybrid approach- PSO implementation incombination with classical clustering techniques like k-means, to optimize the solution.

6. Acknowledgements
A research project to cluster the sunspots using machine learning was suppor ted by agrant from Tsukuba Gakuin University in FY2022 (Kyodo Kenkyu). This research note details apreliminar y investigation to carr y out that research. The author expresses his gratitude to theselection committee, and to the Kiyo committee to get this research note published.
The author would also like to express gratitude to the Debrecen Heliophysical Observatory(http://fenyi.solarobs.csfk.mta.hu/DPD/) for providing daily time series data from 1974 to 2016,and NOAA National Centers for Environmental Information for providing solar flare index data [15].

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筑波学院大学紀要182023[6] de Toma, G. et al., Analysis of sunspot area over two solar cycle, The Astrophysical Journal, 770:89 (13pp),
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