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: