A Statistical review of the dates and patterns of volcanic activity of Lewotolo Volcano, East Nusa Tenggara, Indonesia

Lewotolo is a stratovolcano located on the Lembata Island, East Nusa Tenggara (Lesser Sunda Islands), Indonesia. The first geohistory of the Lewotolo volcanic eruption was recorded in 1660 (Volcanic Eruption Index (VEI) 3). Since November 11, 2020, Lewotolo has been included in the list of Indonesian volcanoes with the necessary precautions, comparable to the Anak Krakatau, Merapi, and Semeru volcanoes. We investigated Lewotolo volcanic activity by analyzing the height of the ash column data, maximum seismograph amplitude, and recorded seismic duration from November 29, 2020, to September 23, 2022, which are provided in magma.esdm.go.id. The results showed 191 records of eruption activity data, which formed three clusters for each variable using the Elbow Method in the Non-Hierarchical K-means clustering analysis. These data were plotted on the solar and Hijri lunar calendars. The data plot shows anomalies in the volcanic activity frequency and a significant pattern of activity at specific times. The data plot illustrates that the value of the activity frequency pattern tends to increase at Earth orbital events such as the December-January perihelion (up to 0.124) and June-July aphelion (up to 0.262) and at the new moon phases (up to 0.168). This phenomenon appears as solar and lunar tidal anomalies that commonly occur as gravitational sea tides. Along with the need for more comprehensive data, the results of this study may provide new perspectives for further research on the possible role of gravitational tide phenomena in volcanic activity, at least to explain the volcanic activity in Lewotolo.


Introduction
On November 29, 2020, at 09:45 local time, larger explosive eruptions occurred on the Lewotolo Volcano on Lembata Island, Indonesia [1,2].Interestingly, this eruption occurred about at the end of the year and coincided with the full Moon date.This condition is the same as that of the Krakatoa destructive eruption followed by the tsunami that occurred at the end of 2018 and during the full moon [3].These eruption events prompted us to further investigate the data record, the level of activity of Lewotolo volcano, and its periodic eruption based on solar and lunar calendars.This study began with suspicion of the possibility of a link between the position of the Moon and the Sun relative to the Earth with specific volcanic activities, such as Lewotolo in November 2020 and Krakatoa in December 2018.In several similar cases, some hypotheses have proposed that this may be related to the anomalous gravitational forces of the sun and moon [4], which may have affected fluidity-magmatic activity, similar to what occurs with sea tides [5][6][7][8][9].Although this theory still needs to be proven further, in this study, we attempt to statistically review the dates of eruptions with the orbital events of the Moon and Sun with respect to Earth.This study aims to IOP Publishing doi:10.1088/1755-1315/1245/1/012006 2 review the pattern of eruption events on lunar and solar calendars based solely on the resulting statistical expressions.Furthermore, the process and mechanism of eruptions must be investigated more comprehensively.

Figure 1.
Location map of Lewotolo volcano on Lesser Sunda, East Nusa Tenggara, Indonesia, and photo documentation of the larger explosive eruption [1], date: November 29, 2020.
Lewotolo Volcano (Ili Lewotolo) located di East Nusa Tenggara (Lesser Sunda), Indonesia.It part of Lembata Island in the Flores Sea (coordinates: 8.274°S, 123.508°E; Figure 1).The Lewotolo is stratovolcano-type [10].It mainly has basaltic andesite lava associated with the Eastern Sunda Arc tectonic setting, part of the Adonara-Pantar segment, a regional subduction zone.Lewotolo is likely associated with calc-alkaline magma origins, which have relatively more fluid characteristics, lower viscosity, and lower N silica content than rhyolitic magma [11].These characteristics led to various Lewotolo eruption types, ranging from vulcanian to strombolian.Recent stromobolian eruptions were recorded in November 2020.The fair-confirmed Holocene eruptivity periods occurred at 1660 at VEI 3, then 1819; October 6 1849; October 5-6 1852; 1864; June 2 1899; 1920, December 15 1951; January 2-14 2012, and lastly continuously well-recorded occured since November 27 2020 [1].Nearly all these periods occurred at about the end of the year (October-Desember).Reports suggest that Lewotolo eruptions are likely to be in the VEI 2.
Several orbital phenomena occur owing to changes in the distance between Earth and the Sun [12].The distance from the Sun changes every day of the year (365.25 days in the Gregorian calendar) because Earth's orbit around the Sun is elliptical.When the Earth is at its closest distance to the sun, it is called a perihelion.When the Earth is at its farthest distance from the sun, it is called an aphelion.Aphelions occurred every year between July 2 and July 7. Perihelions occurred on January 3.There is also something called the equinox, which is divided into two: the March Equinox and the September Equinox [13,14].Astronomically, the March equinox is the point of intersection of the ecliptic and celestial equator that the Sun passes through on its quasi-annual journey from the Southern Hemisphere sky to the Northern Hemisphere sky.The March equinox is also known as the vernal equinox in the Northern Hemisphere and autumnal equinox in the Southern Hemisphere.Similar orbital phenomena can also result from changes in the Moon's position relative to the earth and sun.This phenomenon is divided into several moon phases (such as the new moon phase to the full moon phase), which are viewed based on the appearance of the moon's luminescens visible from Earth [6].This can be described through the lunar calendar, as in hijri month dates [15].
In this study, we aimed to understand the pattern of volcanic eruption activity by statistically reviewing several quantitative parameters, such as the observed height of the ash column and seismograph responses during eruptions, including maximum amplitude and seismograph duration.Data analyses were conducted using k-Means Clustering Algorithms.It is a technique for grouping data such that members of the same group are more homogeneous or more similar to each other than members of different groups [16,17].In addition, the k-means algorithm divides the dataset into k clusters with a given k value, followed by the Elbow Method.It generates specific cluster numbers, which are groups of data that have a smaller distance between data in the group than the distance between data outside the group [18][19][20].The advantage of kmeans clustering is that it is susceptible to implementation and the learning process is complementary and fine for further data interpretation.The k-means algorithm represents each cluster with a centroid or a cluster center.The cluster data and its centroid can be interpreted as a pattern in data expression.

Method
Data Records.In this study, we used well-observed records of Lewotolo eruption activity from open-access data in magma.esdm.go.id, which has officially been reported.The report contains eruption activity, including the date of the event, photos of the volcano when it erupted, height of the visible ash column, and duration and maximum seismograph amplitude when the eruption occurred.The data used in this study were recorded from November 2020 to September 2022 (Appendix 1), totaling 191 eruption events.We plotted the eruption date on the Gregorian date as a solar calendar from the date of the first day at the beginning of the year (starting on January 1) and reviewed the position of the Hijri days as the lunar calendar.In the data record, we statistically reviewed the data using numerical data review, the Elbow Method, and k-Means Clustering.The data were processed using Google Collaboratory and presented in the form of x-y plots.
Elbow Method.This method is used to determine the optimal number of clusters or groups.The Elbow Method considers the Sum of Square Error (SSE) value expressed by the estimated k value (starting at k = 2), which is represented by a line graph.The concept is to start the calculation with k = 2 and then increase each step of k by one step per k unit.The selection of the best k value is based on the lowest angle value (sharper) between the two lines, from k = n to k = n + 1.The change in the value of k, which increased, was followed by a decrease in the SSE value.Thus, the optimal number of clusters can be determined (see Equation 1).
Where, k is the number of clusters, xi is the i-th data value, and μk is the k-th cluster center point value.The changes in the value of k and SSE value are presented in the form of xy line-graphs.

K-means
Clustering.The k-means algorithm is a clustering method of unsupervised learning, in which the similarity measure of data in a group is determined based on the smallest distance of each data point to the centroid of each cluster.The objective function of the k-means clustering algorithm is to minimize the within-cluster variance and maximize the variance between different clusters.The k-means clustering algorithm consists of the following steps: A random value of ݇ as the number of clusters to be formed on the data is determined.The centroid value at the initial stage is determined randomly, whereas in the iteration stage conducted continuously, Equation (2) is used.
Where, μij denotes the average centroid of the i-th cluster for the j-th variable.Ni is the number of members in the i-th cluster.xkj is the k-th data value for the j-th variable in cluster.The proximity of the data to a particular cluster is determined by the distance between the data and cluster center.The centroid distance used is the Euclidean Distance, as shown in Equation (3).

‫ݔ(ܦ‬
Where, D (xi, μ) is the distance between data xi and centroid μi.xij is the ith data point in the jth data variable.μij is the ith cluster centroid of the j-th variable.The data were clustered based on the distance to the nearest centroid.The steps in Equation (2) are repeated until the centroid iteration is optimal, that is, if the cluster center no longer changes (converges to single value), then the clustering process is complete.

Result
The Elbow Method results in an elbow point that determines the optimal value of k for each parameter (height ash column, duration, and maximum seismograph amplitude).It can be seen that the ash column graph forms an elbow at k = 4 with an SSE value = 0.42 x 10 7 , then at k = 5 has a decreasing SSE value and decreases very slowly thereafter.Therefore, the value of k used for the observed ash column height above the summit (meter) consisted of four clusters (k = 4).In the graph of duration of seismograph activity forming an elbow at k = 3 with a value of SSE = 114567.6,at k = 4, the SEE value decreases slowly thereafter.Thus, the k value determined for the duration of the seismograph activity was optimum in three clusters (k = 3).The maximum seismograph amplitude graph forms an elbow at k = 4 with an SSE value of = 1584.0;then, at k = 5, it has a decreasing SEE value and decreases very slowly thereafter.Thus, k used as a cluster on the maximum seismograph amplitude was optimum in four clusters (k = 4), see Figure 2.
Through the results of the k-means clustering analysis with the value of k in each parameter, the data members in each data group/cluster can be determined.Numerically, the centroid of each cluster, the amount of data, the minimum-maximum value, and the standard deviation can be determined.These data groups serve as a reference to distinguish the level of volcanic eruption activity from other eruption events.In this study, we arranged cluster order numbers based on the magnitude of the centroid value in correlation with the eruption activity level.The greater the cluster order value, the higher the eruption activity level.The descriptive statistics of k-means clustering are presented in Table 1 and Figure    Note that the ash column has four clusters; however, in cluster-4, there is only one event (single data).Therefore, we renamed cluster-4 as cluster-3A.In cluster-3A of the ash column, there was only one ash column member with a data value of 4000 m (ID-1).This is because 4000 m is very far from the other data.Thus, these data formed one separate cluster.Seismic duration data formed three clusters.The third cluster of seismic duration only has three members, where the three members are the three longest seismic duration values, namely, 400 s, 500 s, and 600 s.The maximum amplitude data formed 4 clusters.In the fourth cluster, there was the highest value of maximum amplitude, which was 8054 m.The clustering results obtained from the calculation were superimposed on a distribution graph that represents volcanic activity events in both the lunar and Gregorian calendars.Each cluster is defined by a range boundary that is determined by the maximum and minimum values of the data within the cluster.To address the gaps between clusters, we assumed that the median value fell within the cluster boundaries.This study illustrates that higher cluster numbers correspond to greater degrees of volcanic activity, whereas smaller cluster numbers indicate lower levels of activity.Consequently, the findings of this study offer a clearer depiction of the pattern-indicating dates with higher volcanic activity in Lewotolok.Furthermore, the clustering results (as Figure 3) are re-visualized on the activity vs. date graph, as depicted in Figures 4-8.

Discussion
In this study, we reviewed the eruption activity based on three observed parameters: height of ash column, duration of seismograph activity (seismic duration), and the maximum recorded seismic amplitude during eruption.We plotted the eruption data together with the Gregorian calendar (Figure 4 and Figure 5), which represents the Earth revolving to the sun, and the Hijri calendar, which represents the Moon revolving to Earth (Figure 6-8).Some orbital conditions, called perihelion, aphelion, equinox, and soltice, occur in the Earth's orbit with respect to the sun.This phenomenon was repeated every year.This phenomenon is an implication of the shape of the Earth's orbit of the sun, which is elliptical, and the tilt of the Earth's axis against the orbital trajectory [12].The Earth periodically revolves around the sun for 365 days, 6 hours, and 9 minutes (or approximately 365.25 days), and one periodic revolution is referred to as one year, which is divided into 12 months in the Gregorian calendar.
On the solar calendar, every early (3 rd -4 th ) January, perihelion always occurs, which is the position of the earth and sun at a relatively close distance [12].This phenomenon occurred on March 21 st and September 23 rd .Then, the solstice phenomenon occurs when the sun appears to reach its most northerly or southerly excursion relative to the celestial equator on the celestial sphere.Around the end of June (21 st ), the Sun travels along its northernmost path in the sky.At the end of December (21 st ), the sun travels along its southernmost path in the sky.These phenomena are related to the shape of the Earth's elliptical trajectory with respect to the sun and the period of change of the Earth's axis tilt in a one-year cycle [14].Plotting the eruption data of Lewotolo volcano, it can be seen that the eruption frequency often occurs in the middle of the year (June-July) and towards the end of the year (December).The average ash column generated from 191 recorded Lewotolo eruptions was ± 880 m, and most of the ash columns formed from June to December were relatively higher than this value (Figure 5).The maximum recorded value produced by Lewotolo was ± 4000 m in November 2020.In retrospect, the high frequency of eruptions in June and July, the June solstice, and the July aphelion.The frequency of eruptions in December was related to the December solstice and January perihelion (in the following year).Lewotolo eruption activity is relatively small on the equinox, either during the March or September equinox.
The first and second highest volcanic eruptions occurred in December (44/191) and July (36/191), respectively.The first and second highest average seismograph amplitudes occurred in February (32.8 mm) and January (32.2 mm), respectively.Volcanic activity increased from September to December (73/191) (Figure 5).This was followed by several eruptions of ash columns formed at the top of the volcano.The highest ash column height of 4000 m occurred on November 29, 2020, or 14 Rabīʿ al-Awwal 1442, a time relatively close to the end of the year and close to the full moon phase.The lowest volcanic eruption activity occurred from January to March, which was 16/191.On average, the height of the ash column of Lewotolo volcano formed was 876.8 m from the top of the volcano.From the maximum amplitude on the seismogram, it was observed that the eruptions in January had a higher average maximum amplitude, decreased until June, and increased again in July.The amplitude variations produced in July were relatively more diverse, with higher eruption frequency values.Similarly, the December eruption, although with a smaller average, had a relatively higher frequency of eruptions with a more diverse maximum amplitude variation.The high amplitude generated by the seismograph indicates that the amount of friction between the volcanic material and the volcanic magma channel formed when the volcano erupted.As previously discussed, June-July coincides with the aphelion and mid-year soltice, whereas the December-January eruption coincided with the perihelion, December-soltice, and Januaryperihelion.We also reviewed the periodic eruptive activity based on the Moon calendar.The Moon calendar was determined based on the phases of the Moon.The moon phase occurs because of certain conditions in the positions of the Earth, Moon, and Sun.The Moon calendar used in this study is the Hijri calendar.The calendar is determined from the appearance of the new moon, the full moon, until it returns to the new moon phase.Traditionally, the lunar calendar is divided into 30 days, which can be divided into several lunar phases, in order, namely the new moon phase, waxing cresent, 1st quarter moon, waxing gibbons, full moon, waning gibbons, 3rd quarter, waning cresent, and back to the new moon phase (Figure 6-8).This moon phase can be distinguished by the appearance of the moon, which is an implication of the positions of the sun, moon, and earth.When compared with Lewotolo eruption activity, ash columns with a height of >1000 m often occur during the full moon phase and from the new moon phase to the waxing cresent moon phase.The cumulative frequency of eruptions during this phase was also relatively higher than that during the other Moon phases.In addition, it was observed that the amplitude of the eruptions produced during the new moon and full moon phases was relatively more varied.A stark contrast occurred during the full moon phase, where the maximum amplitude recorded on the seismograph was relatively higher than other phases between the two phases.In addition, the graph shows a sinusoidal pattern in the data, which should be further examined in future studies.
Thus far, in the analysis conducted, there is an impression of a special pattern between the eruption parameters used and the orbital moment between the Earth, Moon, and Sun.From the observation span of approximately 2 years, there appears to be a tendency for Lewotolo volcano to have higher eruptive activity at the end of the year.Some of the high eruptive activity is close to the occurrence of the December solstice and January perihelon phenomena.In the middle of the year, eruptions often occur, although not as large as at the end of the year, and the eruption events are close to the phenomena of the june solstice and july aphelion.In the March and September equinox, Lewotolo eruption activity was relatively less frequent.In terms of proximity to the lunar phases, Lewotolo activity appears to increase but is more frequent before and after the new moon.This study revealed the possible interaction between the position of the Moon and Sun with respect to Earth and the eruptive activity of Lewotolo.This is also related to the distance of the earth from the sun during the buli around the sun and the position of the Moon with respect to the Earth and Moon.In the new Moon and full Moon phases, the Earth, Moon, and Sun are aligned.The difference is that in the new moon phase, the moon is between the position of the earth and the sun, whereas in the full moon phase, the earth is between the position of the moon and the sun.Both produce significantly different gravitational pulls; one of the natural phenomena on earth that can be found is the significance of tidal activity during these moon phases.However, we suggest a more comprehensive study of other volcanoes in Indonesia with relatively similar characteristics.We suspect that the fluidity/viscosity of the magma in volcanic system plays a role in responding to the gravitational pull of the sun and/or moon.Additionally, longer and various observations are required to obtain closer observations.

Conclusion
Based on the results and discussion above, the ash column data formed four clusters, the duration of seismograph activity formed three clusters, and the maximum seismograph amplitude formed four clusters.These clusters were formed based on frequency data and patterns of volcanic activity seen in the Gregorian and Lunar Calendar.Activity frequency patterns tend to increase at Earth orbital events such as the December-January perihelion (up to 0.124) and June-July aphelion (up to 0.262) and at the new moon phase (up to 0.168).The results of the statistical analysis suggest a pattern of interaction between certain positions on the Earth, Moon, and Sun that causes an increase in Lewotolo volcanic activity.This interaction is thought to be due to certain gravitational conditions that can affect pressure in the magma chamber.

Figure 2 .
Figure 2. Line graphs of k-value (number of cluster) and sum of square error (SSE) each parameter.The graph shows that the elbow point is relatively more sharply bent, which was determined as the selected cluster number chosen in this study.

Figure 3 .
Figure 3. Visualization of the distribution of clustered data (black circles) and centroids (red triangles)for each parameter of the Lewotolo eruption activity.

Figure 4 .
Figure 4. Distribution of clustered data (blue dots) of the parameters of height of ash column (top) and duration of seismic (bottom) activity during eruption.Data are plotted on the Gregorian calendar with Earth's orbital phenomena toward the sun (yellow streak area).

Figure 5 .
Figure 5. Frequency distribution of eruptions per Gregorian month and maximum amplitude value recorded by the seismograph for each eruption event (black dots).The average maximum amplitude (blue dots) and standard deviation are listed.

Figure 6 .
Figure 6.Distribution of ash column height clustered data (blue dots) on the lunar calendar with respect to the moon phase.

Figure 7 .
Figure 7. Distribution clustered data of the duration of seismograph activities (blue dots) on the lunar calendar with respect to the moon phase.

Figure 8 .
Figure 8. Distribution clustered data of the maximum seismograph amplitude (black dots) on the lunar calendar with respect to the moon phase.Average (blue dots) and its standar deviation are listed.

Table 1 .
Numerical resume of k-means clustering result of each parameter