State transition matrix and Markov-chain diagram for frequent volcanic eruptions: Krakatoa, Indonesia

¹ Sedimentology, Stratigraphy, and Geodynamic Research Group, Department of Geology, Institut Teknologi Sumatera, 35365, Wayhui, Lampung, Indonesia
² Center for Sustainable Development Goals Studies (ITERA SDGs Center), Institut Teknologi Sumatera, 35365, Wayhui, Lampung, Indonesia.
³ Department of Matematics, Institut Teknologi Sumatera, 35365, Wayhui, Lampung, Indonesia.

^* Corresponding author: danni.gathot@gl.itera.ac.id

Abstract

Krakatoa has been a global attraction throughout history. Historical records of eruptions on this volcanic island complex provide thrill and excitement for visitors at once. They are often stunned by sudden eruptions, noticed by columns of ash billowing high into the sky and drawing attention to the scene. However, eruptions such as this also risk visitors of an improper radius. Therefore, in this study, we aimed to reveal the probability pattern of eruptions to sustain preparedness for the worst. Through the Anakrakatau eruption dataset that we collected from 2018 to 2023 [n=540], we propose a transition matrix diagram of eruption events generated from probability analysis. The approach of this method is based on a Markov-chain analysis. This study assessed the period between eruptions and the probabilities of observed column height. In this study, state determination refers to the k-means clustering (k=3) each variable. The results show that there are states that represent the variety of circumstances transitions in frequent small activity eruption. The highest probability achieved at eruption with maximum ash column below 800 m and time gaps between eruptions in less than two days. The results of this study provide new insights into the probability of annual eruptions and provide information for sustainable risk mitigation purposes. This report can be a reference for visitors to the Krakatau area, either for education or research.