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\title{Lagrangian-based trajectory~ modelling of the Hunga Tonga-Hunga Ha'apai
(HTHH) Eruption in ABL using~ meteorological data from mid-week of
January 2022~~~~~~~~}



\author[1,2]{Sarbojeet Bhowmick}%
\author[3]{David Sládek}%
\author[1]{Josef Vojtěch}%
\author[1]{Lada Altmannová}%
\author[1]{Radek Velc}%
\affil[1]{Department of Optical Networks, CESNET, Prague, Czech Republic}%
\affil[2]{Faculty of Environmental Sciences, Czech University of Life Sciences Prague, Czech Republic}%
\affil[3]{Faculty of Military Technology, University of Defence, Brno, Czech Republic}%


\vspace{-1em}



  
  \date{May 17, 2024}


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\sloppy


Key Points:

\begin{itemize}
\tightlist
\item
  Lagrangian-based HYSPLIT modelling system used to estimate volcanic
  ash particle trajectories.
\item
  HYSPLIT simulation took place before and after the massive eruption on
  15\textsuperscript{th} January 2022 (termed as pre-caldera and
  post-caldera respectively in Section 5)
\item
  Volcanic ash particle deposition and volcanic ash particle position
  simulated using HYSPLIT for the HTHH submarine volcano massive
  eruption event.
\end{itemize}

Abstract

Volcano-seismic signals such as long-period (LP) events and tremors are
important indicators for volcanic activity and unrest. Explosive
volcanic eruptions are stunning phenomena that influence the Earth's
natural systems and climate in a variety of ways. This paper discusses
the mid-week January 2022 eruption of the HTHH submarine volcano,
especially on 15\textsuperscript{th} January an event with many impacts
in the region (dynamic, chemical, climate breakdown). Given the
potential for a volcanic eruption to affect climate, the oceanic system,
or climate variability, consistent and understandable modelling of these
exceptional events is critical.

The main objective was to determine the volcanic effects in our
atmospheric boundary layer (ABL) during the multiple eruptive events
occurred on January 2022 at HTHH. Our discussion also contributes to
understanding the underlying Earth system dynamics triggered by
cataclysmic volcanic eruptions. The Hybrid Single-Particle Lagrangian
Integrated Trajectory (HYSPLIT) model system developed by the National
Oceanic and Atmospheric Administration's (NOAA) Air Resources Laboratory
was used to deliberate the effects caused by the multiple eruptions of
HTHH on mid-week of January 2022. Our modelling results include model
trajectories at different frequency levels, volcanic ash deposition and
ash particle position from the series of multiple eruption events of
submarine volcano HTHH in the mid-week of January 2022.

\textbf{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
(14\textsuperscript{th}-18\textsuperscript{th} January 2022). The
magnitude spectrum equation in the frequency domain is computed using
abs (X\textsubscript{f})~from the complex output X\textsubscript{f}. In
contrast, the phase spectrum is derived using angle (X\textsubscript{f})
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 \textbar{}X(w)\textbar{} 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:

\[dU_{i}=a_{i}dt+b_{\text{ij}}d\xi_{j}\]

\[dX_{\text{i\ }}=\ U_{i}\text{dt}\]~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ \ldots{}. Equation 1 (Yaping Shao, 1991)

Here, U\textsubscript{i} and X\textsubscript{i} are the velocity and
position of the particle, respectively; t is time; and d\selectlanguage{greek}ξ\selectlanguage{english}j 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 \selectlanguage{greek}ϵ\selectlanguage{english}* can play a significant role, where the ratio between \selectlanguage{greek}ϵ\selectlanguage{english}* and its
time-averaged value (= \selectlanguage{greek}ϵ\selectlanguage{english}) can reach as high as 50. However, in
Lagrangian stochastic (LS) particle trajectory models have significant
impact on the intermittent behaviour of \selectlanguage{greek}ϵ\selectlanguage{english}*. Thomson (1987); Wilson and
Sawford (1996) studies show that LS models typically do not consider for
the intermittent behaviour of \selectlanguage{greek}ϵ\selectlanguage{english}*. LS models estimate a local Lagrangian
time scale as a function of a local \selectlanguage{greek}ϵ. \selectlanguage{english}Studies from Pope and Chen (1990)
using an extended LS model that includes not only the instantaneous
velocity, but also the instantaneous dissipation (\selectlanguage{greek}ϵ\selectlanguage{english}*) along a particle
trajectory. In this model, where the dissipation rate \selectlanguage{greek}ϵ\selectlanguage{english}* is sampled from
a log-normal probability density function (PDF), by solving an
additional stochastic differential equation for \selectlanguage{greek}χ \selectlanguage{english}[?] \selectlanguage{english}ln(\selectlanguage{greek}ϵ\selectlanguage{english}*/\selectlanguage{greek}ϵ\selectlanguage{english}).

T. Haszpra and T. T\selectlanguage{ngerman}él (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 r\textsubscript{p}(t) for heavy particles with
density p significantly greater than that of the ambient medium are as
follows:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
r\textsubscript{p}~''= 1/St . (v(r,t) - r\textsubscript{p}' -
W\textsubscript{terminal} n) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~\ldots{}. Equation 2 (T. Haszpra and T. Tél,
2011)

where v (r, t) is the flow field, W\textsubscript{terminal} is the
dimensionless terminal velocity in still fluid, and n is an
upward-pointing unit vector. The units of velocity and distance are
characteristic velocity units, U and L, respectively. The dimensionless
relaxation period of inertial particles exposed to Stokes drag is
denoted by the Stokes number (St). Typically, the limit of St0 in
(equation 2) indicates finite acceleration only if the parenthesis on
the right-hand side disappears, and the large-scale equation of motion
for aerosol particles becomes even simpler than before. On the contrary,
the inertial effects are minor, but deposition must be considered with a
terminal velocity in the vertical direction.

In this paper, we used magnitude spectrum to get the relative intensity
of the BH1 frequency channel from HTHH eruption event on
15\textsuperscript{th} January 2022 at 4:12 UTC can be seen in Fig. 1.
For charting vibration spectra, logarithmic amplitude scaling is
preferable to linear amplitude scaling because it allows for better
evaluation of extremely tiny components in a spectrum. Linear amplitude
scaling makes the larger components of a spectrum highly visible and
easy to analyse, but it might make very small components impossible to
perceive. The technique of spectral balancing is used to flatten the
frequency content and amplitude spectra of seismic data. This approach
can increase vertical resolution in seismic amplitude volumes by
revealing narrow channels and visible edges. Following spectral
balancing, energy ratio coherence can be applied to both the input data
and the spectrally balanced data. Spectral decomposition may also be
used to spectrally balanced versions of raw seismic data, allowing equal
time slices to be computed from speech component volumes.

To summarise, spectral magnitude is an energy measurement that
corresponds with the trace in seismic data. The seismic moment and
magnitude can be estimated via spectral analysis as shown in Fig. 1.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}
\caption{{Spectral magnitude graph from the HTHH massive eruption that occurred on
15\textsuperscript{th} January 2022 at 4:12 hrs (UTC)%
}}
\end{center}
\end{figure}

A seismogram's frequency content may be viewed as it varies over time
using a spectrogram. Spectral balancing is a method used in seismic data
to flatten the frequency content and amplitude spectra, enhancing
vertical resolution, and displaying narrow channels and distinct edges.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}
\caption{{Shows the GOES-17 satellite image of the HTHH Eruption that happened on
15\textsuperscript{th} January 2022. Below three images from left to
right are satellite images taken later the massive eruption event on
15\textsuperscript{th} January 2022%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.84\columnwidth]{figures/image4/image4}
\caption{{Shows the spectrogram from the caldera submarine HTHH volcano eruption
that occurred on 15\textsuperscript{th} January 2022 at 4:12 hrs (UTC)
using the BH1 channel data (Data obtained from PyWEED software)%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}
\caption{{Image collected from the LANDSAT 8-9 (Level 2) monitored on January 17,
2022 after the massive eruption of submarine volcano HTHH%
}}
\end{center}
\end{figure}

\par\null

2.1 \emph{Volcanic ash cloud transport}

Submarine eruptions are volcanic eruptions that occur underneath the
water's surface. Due to hotspots, these eruptions can occur near
constructive edges, subduction zones, and within tectonic plates.
Throughout geological history, explosive submarine eruptions have
occurred in a variety of submarine environments. The accompanying
deposits indicate that the eruption of fractured magma-seawater mixes
forms ascending flows that eventually feed an undersea flow and fall
deposits. Deposits from explosive submarine eruptions have been reported
1-4 km below the surface in the deep sea, with both flow and fall
deposits ranging several kilometres over the seafloor. However, there is
no precise information about ''submarine volcano cloud transport''
available. Yet, based on known data on undersea eruptions using HYSPLIT
models, it can be concluded that volcanic ash is transported through
water during a submerged eruption in the same way as it is transported
through air during an aerial eruption. The difference would be that it
would be transported through water rather than the atmosphere.

In the atmospheric sciences field, the HYSPLIT model is a frequently
used atmospheric transport and dispersion model. The model replicates
the dispersion and trajectory of chemicals carried and diffused through
our atmosphere on local to global dimensions. It is intended to
facilitate a wide variety of simulations concerning the movement and
dispersion of pollutants and dangerous compounds in the atmosphere. Data
acquisition delay varies depending on the sensor and method utilized for
real-time monitoring of volcanic ash clouds. The NOAA/CIMSS Volcanic
Cloud Monitoring website, for example, provides near-real-time
processing of multiple geostationary and low-Earth orbit satellites that
cover a large portion of the globe. The delay period for using CATS
near-real-time lidar measurements to monitor volcanic ash clouds is
around 3-6 hours. The use of DB/DR data processing might eventually
lower the temporal lag for day-night monitoring of volcanic
SO\textsubscript{2} and ash clouds. Nevertheless, there is no universal
number for data acquisition latency because it is affected by several
aspects such as the type of sensor, technique, and processing involved.
The utilisation of GEO satellite data is necessary for the early
identification and tracking of volcanic ash plumes and cloud movements.
Volcanic eruptions may now be predicted using thermal infrared remote
sensing technologies. Nevertheless, there is no information on the
typical latency time for monitoring volcanic ash clouds utilizing GEO
satellite data or thermal infrared remote sensing technologies. Early
detection and tracking of volcanic ash plumes and cloud trajectories
requires the use of GEO satellite data. The principal observables of
volcanoes include deformation, surface alteration, gas emissions,
temperature anomalies, and ash clouds. Deformation has been proven to
precede volcanic eruptions in terms of predicting. Because of
high-temporal-resolution geostationary and polar-orbiting meteorological
satellite data, gas emissions and thermal anomalies may be detected in
near-real time. Yet, because of their fluctuating composition and size
dispersion, ash clouds are more difficult to observe. Even with a lag of
one hour owing to propagation time, worldwide infrared monitoring can
offer timely information to Volcanic Ash Advisory Centres (VAAC).
Observational data from satellite remote sensing networks are crucial in
estimating the ash cloud's 4D dispersion. In this paper, we use HYSPLIT
modelling system to monitor the ash cloud trajectories during the event.
To summarize, several factors influence the latency time for monitoring
volcanic ash clouds. They include satellite data difficulties such as
delay and limited access to pictures. Mesoscale scanning can greatly
reduce latency, while distant sensing networks play an important role in
identifying the 4D dispersion of the ash cloud.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ ~ {[}a{]}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ {[}b{]}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~{[}c{]}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~{[}d{]}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ {[}e{]}

Below {[}f{]}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}
\caption{{Figures (a-f), describes the volcanic ash cloud transport in ABL on
15\textsuperscript{th} January 2022 from HTHH submarine volcano eruption
since the beginning of event time at 4:20 UTC and throughout the day
till 15:20 UTC at different timestamps.%
}}
\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

2.2 \emph{Volcanic ash cloud composition}

The rock, mineral, and glass particles that make up volcanic ash are
expelled by a volcano during an eruption. The particles are under 2 mm
in diameter. Rock shards, mineral crystals, and volcanic glass all make
up volcanic ash. The composition of volcanic ash is determined by the
chemistry of the magma from which it generally formed. It has not been
established that most of the minerals found in ash are harmful to human
health. Volcanic ash's chemical makeup changes according to the kind of
volcano and the minerals contained in the magma. In general, from a
stratovolcano volcano, volcanic ash is composed of roughly 65\%
SiO\textsubscript{2}, 18\% Al\textsubscript{2}O\textsubscript{3}, 5\%
Fe\textsubscript{2}O\textsubscript{3}, 2\% MgO, 4\% CaO, 4\%
Na\textsubscript{2}O, and 0.1\% S. In addition to these primary
components, 37 trace metals have been identified, including Ba, Cu, Mn,
Sr, V, Zn, and Zr. Volcanic ash contains fundamental minerals such as
quartz and tridymite, as well as secondary minerals such as kaolin-group
minerals and alunite. Volcanic ash's physical and chemical
characteristics are largely influenced by the eruption style. Basaltic
air-borne pyroclastic materials have a silica content ranging from 45 to
53.5\%, intermediate (andesitic) air-borne pyroclastic materials have a
silica content ranging from 53.5 to 62\%, and felsic (dacitic and
rhyolitic) air-borne pyroclastic materials have a silica content of
greater than 62\%.

In case of submarine volcanoes, they dump massive amounts of stuff into
the oceans, including ash. Volcanic ash has long been detected in marine
sediment, and its chemical composition can be utilized to estimate the
chemical composition of undersea volcanic ash. One strategy is to
quantify distributed volcanic ash in marine sand using geochemical
methods. Another method is to use the chemical makeup of volcanic ash
deposits to determine their origin.

Scientists developed a relationship between the color and chemical
content of discoloured seawater in the vicinity of an underwater
volcano. This approach, however, may not be suitable for identifying the
chemical composition of undersea volcanic ash. Microbial communities
found in sediments differ greatly from those found in hydrothermal
fluids. Volcanic ash, such as that seen in the Kermadec arc, is a kind
of sediment formed by explosive eruptions. Scientists evaluated
microbial community compositions and functioning in two hydrothermal
fluid and one tephra (volcanic ash deposit) samples taken from the
Kermadec arc in research published in Frontiers in Microbiology. The
study discovered that characteristics influencing community structure
and element cycling have a significant influence on local element
cycling, such as sulphur and nitrogen cycling, Fe-S-mineral
precipitation, and the employment of iron (III) as an electron acceptor.
Generally, knowing the chemical composition of undersea volcanic ash
necessitates the use of geochemical approaches or pinpointing its
origins through chemical composition.

2.3 \emph{Volcanic ash particle monitoring}

For the purpose of identifying and tracking volcanic eruptions and ash
in the atmosphere, satellite sensors are crucial. The Advanced Baseline
Imager (ABI) on GOES-16 and GOES-17 is the principal surveillance
instrument for volcanic clouds. VAAC forecasters utilize ABI data to
track clouds whose position, evolution, and/or spectral features
correspond to volcanic activity. Volcanic ash detection and monitoring
are crucial for ensuring safety and reducing economic damage. The height
of a volcanic cloud indicates the severity of an explosive event. Flight
level (FL) represents the top of a laterally expanding volcanic cloud
and is used to report volcanic cloud height. Researchers examine the
average volcanic ash cloud height per occurrence in comparison to that
allocated by the M-ESP database to determine how the activity recorded
within Volcanic Ash Advisory Areas (VAAs) relates to predicted activity
for a specific volcano.

In addition to satellite sensors, a strategy for increased detection of
airborne volcanic ash has been developed based on visible (VIS),
near-infrared (NIR), shortwave infrared (SWIR), mid-wave infrared
(MWIR), long-wave infrared (LWIR), ultraviolet (UV), microwave
radiometry, lidar, radar, or combinations thereof. Remote sensing
technology is used by satellite sensors to detect volcanic ash. For
nearly 20 years, the split window or reverse absorption approach has
been employed. The brightness temperatures recorded using two distinct
wavelengths of infrared light, which react differently when they travel
through clouds of volcanic ash or water droplets, are compared in this
approach. Volcanic cloud monitoring is frequently done using the SEVIRI
sensor on Meteosat Second Generation (MSG) geostationary satellites. It
has a spatial resolution of 3 km at the equator and 4.5 km in
Mediterranean latitudes, and it measures radiances in 12 spectral
channels spanning the visible to infrared spectrums. Thermal infrared
remote sensing can identify volcanic ash clouds fast and precisely.
Unfortunately, the inter-band correlations in remote sensing data are
rather significant, making it difficult to discern between different
types of land cover and atmospheric conditions. Researchers have created
algorithms that employ numerous sensors, including lidar and radar data,
as well as thermal infrared data from satellites, to improve the
accuracy of airborne volcanic ash detection. These algorithms can offer
more precise data on the position, height, and concentration of volcanic
ash clouds.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}
\caption{\selectlanguage{polish}{Pressure waves source from HTHH submarine volcano eruption on 15th
January 2022 recorded by two USGS Hawaiian Volcano Observatory (HVO)
infrasound sensors located south of Kīlauea volcano summit%
}\selectlanguage{english}}
\end{center}
\end{figure}

Pressure waves from the event shows the highly compressional waves
originated from the massive eruption that occurred on
15\textsuperscript{th} January 2022. The nuclear bomb like explosion
occurred at submarine volcano HTHH shows the flow of waves with a high
velocity as shown in Fig. 6. There are various advantages to using
HYSPLIT for volcanic ash monitoring. Firstly, by merging satellite
retrievals with HYSPLIT models, it can enhance volcanic ash forecasts.
Second, it can assist lessen the effects of volcanic ash on aircraft by
giving precise ash deposition projections. Eventually, it may be
utilised to account for aggregation in tephra-deposit model projections
by adjusting particle-size distributions. Lastly, it can assist
distinguish between phreatic and phreatomagmatic eruptions by offering
insights into eruption mechanisms.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}
\caption{{Shows volcanic ash particle deposition (mg/m\textsuperscript{2}) of
16\textsuperscript{th} January 2022 after the massive eruption on 15
January 2022 at HTHH submarine volcano. This volcanic ash particle
deposition (mg/m\textsuperscript{2}) plot obtained using READY of
HYSPLIT by NOAA ARL%
}}
\end{center}
\end{figure}

Overall, adopting HYSPLIT for volcanic ash monitoring is a useful
technique for limiting the dangers posed by volcanic ash on flying
aircraft. It gives precise volcanic ash deposition projections and aids
in the differentiation of different types of eruptions.

3. Data, or a descriptive heading about data

HYSPLIT is a comprehensive system for simulating basic air parcel
trajectories as well as sophisticated transport, dispersion, chemical
transformation, and deposition scenarios. The HYSPLIT modelling system
has already been used to track and forecast the release of radioactive
material, wildfire smoke, windblown dust, pollutants from various
stationary and mobile emission sources, allergies, volcanic ash, and
simulation of atmospheric tracer release studies. The Air Resources
Laboratory of NOAA created HYSPLIT. Volcanic ash cloud transport during
the mid-week of the event has been simulated using HYSPLIT modelling
system.

In this work, the HYSPLIT dispersion model is used to forecast volcanic
ash movement and dispersion. To deliver information to VAACs, the
National Weather Service (NWS) runs the HYSPLIT model with a unit mass
release rate. The wind pattern above and around the volcano, on the
other hand, is a key source of mistake in estimating where airborne
volcanic ash will travel and settle. Scientists are employing satellite
retrievals to incorporate data into the HYSPLIT model to enhance
volcanic ash forecasts. Quantitative ash distribution projections may be
given by objectively and ideally calculating the volcanic ash dispersal.
MODIS satellite retrievals, for example, were used to assess the HYSPLIT
model's performance in predicting the 2008 Kasatochi volcanic ash
clouds.

Meteorological data files are accessible from a variety of sources,
however the majority of them must be reformatted before they can be used
by HYSPLIT. Conversion applications in the HYSPLIT suite can be used to
convert user-generated meteorological data to HYSPLIT format. In
HYSPLIT, the Meteorology/Convert to ARL menu tab offers numerous choices
for converting meteorological data. This data can be in Gridded Binary
Format (only GRIB-1 is supported by the GUI), Network Common Data Form
(NetCDF), or proprietary binary formats, such as NCAR's MM5.

HYSPLIT requires meteorological data at several heights and time periods
across the simulation's lifetime on an equally spaced grid
(latitude-longitude or conformal projection). The convert to ARL option
in HYSPLIT may convert gridded meteorological data on a
latitude-longitude grid or one of three conformal projections to ARL
format.

The HYSPLIT User's Handbook describes how to transform meteorological
data for usage with HYSPLIT in detail. The manual offers
context-sensitive assistance throughout the graphical user interface,
commonly asked problems, and a list of utility tools such as file
conversion and graphics creation. HYSPLIT is a full framework for
calculating complicated dispersion and deposition trajectories. HYSPLIT
requires meteorological data at several heights and time periods on an
equally spaced grid (latitude-longitude or conformal projection)
throughout the simulation. Meteorological data can be collected from a
variety of sources that have already been prepared for use by HYSPLIT,
or each user can convert their own data to the appropriate format.

NOAA provides source code and PC executable applications for converting
meteorological data from diverse forms to a common format that HYSPLIT
may use. NOAA also supplies UNIX converter programmes. The NOAA website
provides access to HYSPLIT particle trajectories and footprint data.
These data include footprints, which show locations where air parcels
have come into touch with the Earth's surface within a specific
time-period, and particle trajectories, which reflect an air parcel's
passage across space through time.

In brief, HYSPLIT requires meteorological data on an equally spaced grid
at several heights and time periods throughout the simulation.
Meteorological data can be collected from a variety of sources that have
already been prepared for use by HYSPLIT, or each user can convert their
own data to the appropriate format.

4. Results, or a descriptive heading about the results

This model is designed to calculate the transport and dispersion of
volcanic ash from the volcano peak to the column top. Within 0.1 degree
of longitude, height, and latitude, the model estimates the position of
computational particles. The accuracy of HYSPLIT output is based on the
initialization accuracy: the beginning location, size distribution, and
vertical profile of ash particles.

The HYSPLIT model performed interactively in this paper using the READY
website and partially via script. The interactive map compares
horizontal and vertical positioning, with colour denoting particle
height. ARL based satellite data on volcanic ash clouds helps to enhance
HYSPLIT volcanic ash forecasts. HYSPLIT simulation works for volcanic
ash dispersion modelling as following conditions: eruption input,
meteorological data input, ash particle distribution, ash cloud, reduced
ash, and model output. In this work, the Windows-based HYSPLIT modelling
system for volcanic- ash trajectories, ash particle deposition and ash
particle position which includes single or multiple (space or time)
simultaneous trajectories, optional grid of initial starting locations,
computations forward or backward in time and default vertical motion
using omega field. Ash particle position include motion options:
isentropic, isosigma, isobaric and isopycnic in which trajectory
ensemble using meteorological variations and the output of
meteorological variables along a trajectory and trajectory clustering
option for volcanic ash particle deposition.

Using HYSPLIT modelling system we get below results from the simulation
with Fig.7. which include figures i-v showing the volcanic ash particle
deposition from the multiple eruptions that happened on
14\textsuperscript{th} January 2022 to 18\textsuperscript{th} January
2022 at submarine volcano HTHH. Figures vi-x shows the volcanic ash
particle trajectories and figures xi-xv illustrates the ash particle
positions from the same series of multiple eruptions occurred at HTHH
submarine volcano.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image14/image14}
\caption{{(i)%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image15/image15}
\caption{{(ii)%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image16/image16}
\caption{{(iii)%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image17/image17}
\caption{{(iv)%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image18/image18}
\caption{{(v)%
}}
\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image19/image19}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image20/image20}

\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ (vi) and (vii)\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image21/image21}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image22/image22}

\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~(viii) and (ix)\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image23/image23}

\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ (x)\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image24/image24}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image25/image25}

\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ ~ ~(xi) and (xii)\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image26/image26}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image27/image27}

\end{center}
\end{figure}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ (xiii) and (xiv)

\par\null

Below (xv)\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image28/image28}
\caption{{Figures (i-v or 8-12) shows the volcanic ash particle deposition
occurred on 14\textsuperscript{th} January 2022 to
18\textsuperscript{th} January 2022 at HTHH submarine volcano multiple
eruptions. Figures (vi-x) depicts the volcanic ash particle trajectories
from the same event and figures (xi-xv) for the ash particle positions
that occurred between 14-18 January 2022 at HTHH submarine volcano.%
}}
\end{center}
\end{figure}

\par\null

5. Conclusions

In this paper, the simulation results have been analysed. The
simulations estimated using HYSPLIT modelling system has been carried
out for submarine HTHH volcano activity from
14\textsuperscript{th}January to 18\textsuperscript{th} January 2022
(mid-week of January 2022 focusing the multiple eruption events. The
investigations specifically based on:

\begin{itemize}
\tightlist
\item
  volcanic ash particle deposition,
\item
  volcanic ash particle trajectories, and
\item
  volcanic ash particle positions.
\end{itemize}

The results from the simulations can be divided into two parts basically
with the pre-caldera volcanic activity, i.e., before massive eruption on
15\textsuperscript{th} January 2022. The simulations of
14\textsuperscript{th} January 2022 for volcanic ash particle -
deposition, trajectories and particle position can be coined as
`pre-caldera' volcanic activity. Generally during `pre-caldera' volcanic
activity several more eruptions, including lava flows, ash plumes, and
explosive eruptions, may occur during the pre-caldera period of the
volcano. The scale of the volcano may grow over time as more material is
added to the cone, and the eruption types may vary as the magma chamber
underneath the volcano changes.

Investigations for pre-caldera volcanic activity gain a better
understanding of the processes that lead up to a big eruption and to try
to forecast when a volcanic caldera will form. Seismometers, GPS
equipment, gas sensors, and satellite photos usually use to precisely
monitor the volcano's behaviour and follow any changes in activity. The
collapse of the top may create a new conduit for magma to reach the
surface, resulting in a fresh period of volcanic activity after the
construction of a caldera. Furthermore, the collapse may expose new weak
points in the volcano's structure, rendering it more vulnerable to
future eruptions. Yet, depending on the exact volcano and the
surrounding geology, the specific conditions that contribute to
post-caldera volcanic activity might vary greatly.

The HYSPLIT modelling system for HTHH submarine volcanic activity in the
mid-week of January 2022 multiple eruptions has been focused to get
clearance reports from the simulated results in order to make volcanic
ash forecasting results more visualized. Based on the eruption event
simulations HYSPLIT modelling system proves that how monitoring system
parameters are in operations and how the forecasting analyser works with
the HTHH submarine volcanic activity data set for multiple eruptions.

Fig. 8 (figures xi-xv), comprises the volcanic ash particle positions of
submarine HTHH volcanic activity before and after massive eruption
occurred on 15\textsuperscript{th} January 2022. The volcanic ash
particles go \textless{}12000 m layer (AGL) on
14\textsuperscript{th}January 2022 simulation result as in Fig. 8. of
figure xi, whereas figure xii-xv the post-caldera state starts after the
massive eruption on 15\textsuperscript{th} January 2022 the ash
particles go \textgreater{}12000 m layer of AGL. The volcanic ash
particle trajectories, fig. 8 (figures vi-x) shows the ash particle
deposition level in the stratosphere goes \textgreater{}90\% even before
and after the massive eruption event of 15\textsuperscript{th} January
2022. HYSPLIT outputs have more detailed impression of accuracy that's
why the large uncertainties in the eruption parameters i.e., the
volcanic ash particle deposition has shown impact as seen in Fig. 8
(figures i-v) where the ash cloud composite increased by 75\% after the
massive eruption on 15\textsuperscript{th} January 2022 where the
difference can be clearly visible in Fig. 8 (figures i, iii and iv).
More than 300,000 volcanic trace particles per day were released during
the multiple eruption times of mid-week of January 2022 and can be seen
from the simulation results.

\textbf{6. Future Accomplishments}

In our study, we focused on utilizing the HYSPLIT modelling system with
GDAS meteorological data, volcanic ash cloud composite, ash cloud
trajectory frequency, and ash particle positions, which are discussed in
Section 4 of the paper. Additionally, we generated event time
seismograms using PyWEED, as shown in Figure 3.

Regarding seismic activity in the Czech Republic, there is potential for
implementing a machine learning-based sensing system using optical
fibres as seismic sensors. In the western part of the country,
particularly in the Nov\selectlanguage{ngerman}ý Kostel region, there is a history of frequent
earthquakes with magnitudes below 4 occurring throughout the year. This
presents an opportunity for deploying new fibre sensing methods in our
country, as we have access to optical fibre lines that are commonly
shared for research activities. Dedicated parts of the spectrum are
being tested for various research transmissions, including sensing, QKD
(Quantum Key Distribution), and Precise Time and Frequency transfers,
leaving room for cost-efficient solutions for future research
endeavours.

Collaboration with well-established and recognized volcano regions,
which possess comprehensive sensing data, could provide valuable
insights and more precise methods for volcanology. Optical fibre sensing
methods offer the potential for acquiring essential data on gas content
and composition in seismic activity regions worldwide.

The CESNET2 network in the Czech Republic already applies advanced
applications for sensing in the Temelín nuclear power plant,
specifically for containment stability measurements. This involves
ultra-stable frequency transfers between the National Metrology
Institution and the containment sensors. While the project primarily
focuses on the stability of the containment itself, it also considers
seismic events, including earthquakes.

To compare the situation during the eruption events of the HTHH
submarine volcano, we examined seismic activity on the other side of the
Earth, specifically in central Europe, where our locality is situated.
Figure 9 demonstrates a seismograph recording an earthquake activity
with a magnitude of 2.8 at 02:54:47 UTC on January 15th, 2022, near the
Aschach area, northwest of Linz. This earthquake activity was also
monitored for the safety of the nearby Temelín nuclear power plant.
Although these seismic activities generally have ''low'' magnitudes,
they tend to be long-lasting and occur throughout the year. CESNET, as
the Czech NREN (National Research and Education Network) provider,
actively engages with advanced technologies to achieve more precise
measurements and is open to further collaboration within the field.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image29/image29}

\end{center}
\end{figure}

Fig. 9. Seismograph of 2.8 (ML) near Aschach, north-west of Linz.,
Austria near the border of Czech Republic (15\textsuperscript{th}January
2022, 02:54:47 UTC)

\textbf{Acknowledgments}

This work is partially supported by Ministry of Education, Youth and
Sport of the Czech Republic by the project ``E infrastructure
CESNET-modernization'', reg. no. CZ.02.1.01/0.0/0.0/16\_013/0001797 and
in part by the TiFOON 18SIB06 Project through the EMPIR Programme
co-financed by the participating states.\textbf{~}

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