Plain Language Summary
The submarine volcano HTHH had a significant impact on volcano-seismic activity over an extended period of time. The volcanic activity and resulting unrest had diverse effects on Earth’s climate and other crucial natural processes. Seismic events from multiple eruptions influenced dynamic activity, chemical composition, and ultimately led to climate changes. The potential of submarine volcano eruptions to disturb the oceanic system, affect climate, and induce climate variability is exceptional. It is crucial to develop consistent and specialized analytical models to understand the hidden effects of multiple HTHH events on the Earth’s system. In our study, we analysed the outcomes using the HYSPLIT modelling system in the Atmospheric Boundary Layer (ABL), which was activated by explosive tremor events in HTHH. The use of HYSPLIT by NOAA facilitated the modelling of the effects of multiple explosive eruptions of HTHH during that period. The results encompassed trajectories at various altitudes, volcanic ash deposition, and the positioning of volcanic ash particles. For future planning of volcanic explosive events and understanding their climatic aftermath, the modelling results from this study can offer valuable insights in the HTHH volcanic region.
1. Introduction
The submarine volcano HTHH experienced multiple eruptions, which are often accompanied by various seismo-volcanic signals, including very long-period (VLP) events, long-period (LP) events, volcano-tectonic (VT) events, and tremor. These signals provide valuable information about the physical processes occurring at depth and are used to assess the activity state of a volcano. Monitoring observatories continuously analyse these events, considering factors such as their number, amplitude, location, and temporal variations, for early warning purposes.
Each type of volcano-seismic event has distinct characteristics and underlying processes. VT earthquakes exhibit a broad frequency content between 2 and 20 Hz and have an impulsive onset, like tectonic earthquakes. LP events occur in a narrow frequency band of 0.5 to 5 Hz, with a dominant frequency content between 0.5 and 2 Hz. The source process of LP events is still a topic of debate. VLP events share waveform similarities with LP events but have frequencies ranging from 0.01 to 0.5 Hz. Tremor is a long-lasting, emergent seismic signal that can exhibit a broad or harmonic frequency content, showing spectral characteristics like LP events.
Volcano observatories employ seismic sensor networks or arrays to detect and locate these transient and continuous signals. VT events are located using P and/or S wave arrival times, while LP events are located using polarization analysis, P-wave picking, waveform similarity-based methods, or amplitude decay analysis. Tremor is located based on seismic amplitude decrease or phase shifts within a network or seismic array. Conventional seismic monitoring on volcanoes typically involves networks equipped with translational sensors, while portable rotational sensors record ground rotation rates around three axes.
The Lagrangian Transport Model (LTM) used in this study employs Lagrangian calculations based on a reference frame that moves with the river flow. This approach avoids the need for numerical calculation of the convective component of the convection-diffusion equation. In this paper, we utilized HYSPLIT as an LTM to generate backward air mass trajectories up to a specific height, which is crucial for simulating pollution transport. Specifically, HYSPLIT 4 was employed as an LTM to simulate the transport and dispersion of volcanic ash and gases during the studied event.
LTMs have been widely used in research, including studies on volcanic sulphur dioxide (SO2) emissions. Researchers have utilized HYSPLIT to model the transport and dispersion of volcanic SO2 from different volcanoes. Their simulations showed good agreement with satellite measurements, highlighting the effectiveness of Lagrangian-based trajectory modelling in predicting volcanic SO2 injections.
Lagrangian-based trajectory modelling, such as the HYSPLIT model, offers valuable advantages for calculating the injection and dispersion of volcanic gases and particles. Numerous case studies have demonstrated its effectiveness in enhancing our understanding of the environmental and climatic impacts of volcanic eruptions. Compared to other models, Lagrangian-based HYSPLIT modelling provides several benefits that are specific to the scientific application.
One key advantage is the ability to achieve a high level of physical realism. Lagrangian models can capture sub-grid scale information that may be missed by other models. This allows for a more detailed representation of the processes involved in gas and particle transport during volcanic eruptions. Additionally, Lagrangian models exhibit numerical stability, meaning they introduce less artificial diffusion compared to Eulerian-based models.
HYSPLIT, like other conservation models, ensures mass and energy conservation throughout the simulation. This is crucial for accurately representing the physical behaviour of volcanic emissions. Furthermore, HYSPLIT demonstrates computational efficiency and can easily handle complex geometries, making it suitable for studying air deposition and trajectory levels. Its ability to accurately track particle movement in the atmosphere contributes to its usefulness in analysing volcanic ash dispersion, as demonstrated in this study.
2. Composition of the ash particle trajectories
This paper focus on the volcanic ash particle trajectory at different frequency levels for multiple eruptions that occurred at the submarine volcano HTHH specifically mid-week of January 2022 (14th-18th January 2022). The magnitude spectrum equation in the frequency domain is computed using abs (Xf) from the complex output Xf. In contrast, the phase spectrum is derived using angle (Xf) and indicates the phase shift of each frequency component of a signal. Using Fourier transform, the obtained signal converted from the time domain to the frequency domain, where it could be expressed as a complex frequency function. The amplitude of that component is the modulus of this complex function, and its argument is the relative phase shift of that wave. In addition to being easier to solve algebraically, seeing a system via the lens of frequency may frequently provide an intuitive insight of its qualitative behaviour. The magnitude spectrum equation is used to determine the relative intensity of frequency components in a signal. The magnitude spectrum is calculated by multiplying the magnitude of the analytic signal by its phase angle. The magnitude spectrum is shown by a plot of |X(w)| versus w, where X(w) is the Fourier transform of the signal x(t).
The HYSPLIT model system is essentially based on Lagrangian dispersion models, which offered descriptive predictions for air pollution distribution in both homogeneous and inhomogeneous turbulent airflows. The Lagrangian dispersion model, which is based on a simulation of tracer trajectories, naturally describes pollutant transport and is numerically simple. Based on Thomson (1987) the Lagrangian model unfolds the characteristics on the movement of a passive particle in a turbulent flow which can be adequately described by a nonlinear stochastic equation system as follows:
\[dU_{i}=a_{i}dt+b_{\text{ij}}d\xi_{j}\]
\[dX_{\text{i\ }}=\ U_{i}\text{dt}\]                                                                                  …. Equation 1 (Yaping Shao, 1991)
Here, Ui and Xi are the velocity and position of the particle, respectively; t is time; and dξj is a random acceleration. The coefficients ai and bij are determined by the structure of turbulence. Using this method, a complete understanding of atmospheric turbulence over uniform surfaces has been achieved and this has provided a solid basis for the application of Lagrangian models. In this paper, volcanic ash particle trajectories (See in Section 4) have been obtained using HYSPLIT.
Lagrangian models of tracer-particle trajectories in turbulent flows can be adapted for simulation of particle trajectories. This is conventionally done by replacing the zero mean fall speed of a tracer-particle with the terminal speed of the particle. Such models have been used widely to predict spore and pollen dispersal (Andy M. Reynolds et al., 2018). In ABL, Pope (2000) proposed that intermittency in ϵ* can play a significant role, where the ratio between ϵ* and its time-averaged value (= ϵ) can reach as high as 50. However, in Lagrangian stochastic (LS) particle trajectory models have significant impact on the intermittent behaviour of ϵ*. Thomson (1987); Wilson and Sawford (1996) studies show that LS models typically do not consider for the intermittent behaviour of ϵ*. LS models estimate a local Lagrangian time scale as a function of a local ϵ. Studies from Pope and Chen (1990) using an extended LS model that includes not only the instantaneous velocity, but also the instantaneous dissipation (ϵ*) along a particle trajectory. In this model, where the dissipation rate ϵ* is sampled from a log-normal probability density function (PDF), by solving an additional stochastic differential equation for χ ≡ ln(ϵ*/ϵ).
T. Haszpra and T. Tél (2011) discovered that the Maxey-Riley equations yield the equations of motion for tiny, inertial, spherical particles of radius r in a viscous fluid advected by a flow deterministically (M. Farazmand and G. Haller, 2014). The dimensionless equations for the particles trajectory rp(t) for heavy particles with density p significantly greater than that of the ambient medium are as follows: