2 − 1 Volcanic islands, submarine volcanoes, and target areas
We conducted two particle simulation experiments. In the first, particles were tracked from Fukutoku-Oka-no-Ba (24.3°N, 141.5°E) to Iriomote Island (23.98–24.58°N, 123.55–124.15°E), Okinawa (26.00–27.00°N, 127.47–128.47°E), Genkainada (33.30–34.00°N, 129.35–130.35°E), Bungo Channel (32.87–33.27°N, 131.83–132.53°E), off Cape Shionomisaki (33.20–33.50°N, 135.46–136.06°E), and Hahajima Island (26.35–26.95°N, 141.85–142.45°E). The purpose of this experiment was to validate our simulation by comparing the simulated pumice raft arrival dates at the six target areas with those that followed the January 1986 Fukutoku-Oka-no-Ba eruption, which ejected pumice during 18–21 January (Ossaka 1991). Pumice clasts produced by that eruption were observed at Hahajima on 15 March, Okinawa in late May, Iriomote Island on 15 June, Bungo Channel on 26 June, off Cape Shionomisaki in August, and Genkainada in October (Yoshida et al. 1987; Kato 1988).
In the second set of experiments, particles were tracked from major volcanic islands and submarine volcanoes. We selected seven volcanoes: the submarine volcano NNE of Iriomotejima (24.5°N, 123.8°E); the Izu-Tobu volcanic range (35.0°N, 139.1°N); Miyakejima (34.1°N, 139.5°E); Bayonnaise Rocks (31.9°N, 140.0°E); Nishinoshima (27.2°N, 140.9°E); Kaitoku Seamount (26.1°N, 141.1°E); and Fukutoku-Oka-no-Ba. From these volcanoes, we released particles to 16 target areas to estimate pumice raft arrivals. We selected 11 areas important to sea traffic based on the ship-tracking site https://www.marinetraffic.com/: Osumi Strait (30.73–31.23°N, 130.70–131.20°E); Koshiki Strait (31.54–32.14°N, 129.88–130.18°E); Bungo Channel, off Cape Shionomisaki, Irago Channel (34.07–34.67°N, 136.88–137.38°E); off Izuoshima Island (34.60–35.10°N, 138.86–139.86°E); off Cape Omaezaki (34.40–34.70°N, 137.94–138.34°E); off Onahama (37.10–37.70°N, 141.00–141.30°E); off Sakaiminato (35.48–35.88°N, 132.75–133.35°E); Wakasa Bay (35.46–35.86°N, 135.20–136.10°E); and Tsugaru Strait (41.20–41.80°N, 139.92–141.07°E). We selected Iriomote Island, Minami-Daito Island (25.57–26.17°N, 130.92–131.52°E), Okinawa, and Amami Oshima Island (27.64–28.64°E, 128.82–129.82°E) because their economies depend on marine activities and beach tourism, and Chichijima Island (26.77–27.37°N, 141.91–142.51°E) because the only transportation to the island is by sea. The locations of the selected volcanoes and target areas are shown in Fig. 1 and reported in Tables 1 and 2. Figure 1 also shows the paths of the Kuroshio Current and the Kuroshio Recirculation, which are known to affect pumice dispersion (Tada et al. 2021).
Table 1
Volcanic island and submarine volcano sources used in this study. Descriptions are based on Ossaka (1991).
Name | Abbrev. | Latitude, longitude | Representative activity producing pumice rafts |
Submarine volcano NNE of Iriomotejima | IR | 24.5°N, 123.8°E | 1924 |
Izu-Tobu Volcanoes | IZ | 35.0°N, 139.1°N | 1989 |
Miyakejima | MI | 34.1°N, 139.5°E | 1983 |
Bayonnaise Rocks | BA | 31.9°N, 140.0°E | 1952–1953, 1970 |
Nishinoshima | NI | 27.2°N, 140.9°E | 1973–1974 |
Kaitoku Seamount | KA | 26.1°N, 141.1°E | 1981 |
Fukutoku-Oka-no-Ba | FU | 24.3°N, 141.5°E | 1917, 1986, 2021 |
Table 2
Target areas selected for the first and/or second particle tracking simulation experiments.
Name | Experiment | Latitude, longitude |
Iriomote Island | 1st and 2nd | 23.98–24.58°N, 123.55–124.15°E |
Okinawa | 1st and 2nd | 26.00–27.00°N, 127.47–128.47°E |
Genkainada | 1st | 33.30–34.00°N, 129.35–130.35°E |
Bungo Channel | 1st and 2nd | 32.87–33.27°N, 131.83–132.53°E |
Off Cape Shionomisaki | 1st and 2nd | 33.20–33.50°N, 135.46–136.06°E |
Hahajima Island | 1st | 26.35–26.95°N, 141.85–142.45°E |
Osumi Strait | 2nd | 30.73–31.23°N, 130.70–131.20°E |
Koshiki Strait | 2nd | 31.54–32.14°N, 129.88–130.18°E |
Irago Channel | 2nd | 34.07–34.67°N, 136.88–137.38°E |
Off Izuoshima Island | 2nd | 34.60–35.10°N, 138.86–139.86°E |
Off Cape Omaezaki | 2nd | 34.40–34.70°N, 137.94–138.34°E |
Off Onahama | 2nd | 37.10–37.70°N, 141.00–141.30°E |
Off Sakaiminato | 2nd | 35.48–35.88°N, 132.75–133.35°E |
Wakasa Bay | 2nd | 35.46–35.86°N, 135.20–136.10°E |
Tsugaru Strait | 2nd | 41.20–41.80°N, 139.92–141.07°E |
Minami-Daito Island | 2nd | 25.57–26.17°N, 130.92–131.52°E |
Amami Oshima | 2nd | 27.64–28.64°E, 128.82–129.82°E |
Chichijima Island | 2nd | 26.77–27.37°N, 141.91–142.51°E |
2–2 Particle tracking experiments
In our particle tracking simulations, we used horizontal velocities, sea temperatures, and salinities from the ocean reanalysis dataset, a daily dataset with horizontal resolution of 0.1° × 0.1° provided by the operational numerical weather prediction of the Japan Meteorological Agency (JMA, 2013; http://www.jma.go.jp/jma/jma-eng/jma-center/nwp/outline2019-nwp/index.htm). We released particles at 0.5 m depth in all simulations because pumice clasts are usually observed drifting on the sea surface. In the first experiment, batches of 49,000 particles were released from Fukutoku-Oka-no-Ba once per day during 18–21 January 1986. In the second set of experiments, batches of particles were released from the seven selected volcanoes on the 15th day of each month from 1982 to 2015. Batches of 49,000 particles were released from the submarine volcano NNE of Iriomotejima, Miyakejima, Bayonnaise Rocks, Nishinoshima, Kaitoku Seamount, and Fukutoku-Oka-no-Ba, and batches of 18,000 particles were released from the Izu-Tobu range. We selected 49 grids that are in a square shape that is centered at each volcano, with the sides 0.7º long and with each side. The interval of grids is 0.1º that is same as the horizontal resolution of the ocean dataset. 1000 particles are put in each grid. Only for Izu-Tobu, since the volcano is close to the land, we selected 18 grids near the volcano. In both experiments, the particles were assigned drift durations of 365 days because drifting pumice clasts tend to weather into smaller fragments that are no longer buoyant within a year (Kuroda 1987). Each particle’s location was recorded every day, and the first day when any particle arrived in a target area was recorded as a pumice raft arrival.
Particle locations were traced using the formulae:
\({x}_{n+1}={x}_{n}+{u}_{n}{\Delta }t+{\lambda }_{x}\) | (1) |
\({y}_{n+1}={y}_{n}+{v}_{n}{\Delta }t+{\lambda }_{y}\) | (2) |
\(\left({\lambda }_{x},{\lambda }_{y}\right)={P}_{\text{N}}\sqrt{2{\Delta }t}\left(\sqrt{{A}_{\text{H}}^{x}},\sqrt{{A}_{\text{H}}^{y}}\right)\) | (3) |
where (xn, yn) is the horizontal particle location (x and y being the east–west and north–south coordinates, respectively) at time step n; un and vn are the eastward and northward velocities, respectively; and Δt is the time step, taken here to be 20 min. (λx, λy) is the random walk displacement represented by Eq. (3), in which (\({A}_{\text{H}}^{x}\), \({A}_{\text{H}}^{y}\)) and PN are the horizontal eddy diffusion coefficients and the probability function of the normal distribution, respectively. The magnitude of the lateral diffusivity is 100–10,000 m2⁄s (Nummelin et al. 2021). We conducted tests using various diffusivities within that range and compared the results with the record of pumice raft arrivals from the 1986 Fukutoku-Oka-no-Ba eruption. Based on the results of those tests, we set both \({A}_{\text{H}}^{x}\) and \({A}_{\text{H}}^{y}\) to be 1,000 m2⁄s in all experiments.
We represented the number of particles arriving at each target location and their drift durations as monthly and yearly mean values. Monthly means were taken as the average from 1982 to 2015 for each month, and yearly means as the average monthly mean value from January to December.