Keywords

1 Introduction

The number of large-scale oil spill incidents involving tankers has decreased from the 1970s to the 2000s, but is not yet zero [1]. Therefore, large-scale oil spill incidents seem likely to happen in the future. The Ministry of Land, Infrastructure, Transport, and Tourism in Japan (MLIT) has three large-scale oil recovery vessels. These vessels cover any area around Japan within 48 h to prepare for oil recovery following a large-scale oil spill incident. We developed a numerical simulation model called OILPARI [2] for predicting the spilled oil transport on the sea surface to support spilled oil recovery operations by these oil recovery vessels. The past study [2] has proven that OILPARI's simulation accuracy is high.

In the early stages of development, OILPARI was constructed as a stand-alone simulation system (sa-OILPARI) [3] and we started real-time prediction by sa-OILPARI in 2014. OILPARI used datasets delivered by the Japan Meteorological Agency (JMA) concerning ocean currents, winds, and waves as the inputs for the real-time prediction. Owing to the update for a longer forecast period and high resolution of computational grids from JMA, it was already necessary to update the OILPARI simulation system from the beginning of its development [3]. In addition, owing to the demand for the OILPARI simulation system for the examination of seasonal oil transport characteristics and tabletop training for oil spill responses, a system able to perform long-term simulations of past conditions was required. Furthermore, users requested an ability to operate the simulation system as web application rather than as a stand-alone software installed on a local computer.

In this study, we updated sa-OILPARI to incorporate the latest ocean current and wind datasets and improved it to allow for long-term simulations of the past. We also developed a web application-type OILPARI (net-OILPARI). We applied the OILPARIs to an oil spill incident that occurred off the coast of Hachinohe in August 2021 and the pumice stone (floating stone) disaster in 2021.

2 Simulation Model of OILPARI

2.1 Outline of Simulation Model

In this section, the OILPARI algorithm is explained with reference to our previous study [2]. OILPARI adopts a particle tracking method to calculate the oil transports owing to advection by sea surface currents, mechanical spreading of the oil, and turbulent diffusion. The surface currents are generated by currents, winds, and waves. In advection terms, OILPARI includes the effects of ocean currents, tidal currents, and wind-induced currents as effective terms for the oil advection. net-OILPARI includes not only the previously mentioned three components, but also the wave effect (as a Stokes drift). Oil spilled on a water surface spreads according to gravity (buoyancy) and surface tension and diffuses according to turbulence. These effects are called “mechanical spreading” and “diffusion,” respectively. The spilled oil is assumed as an aggregation of particles, and the oil advection, spreading, and diffusion are simulated using a Lagrangian method. The position Xit of particle i at time t is calculated using the movement velocity Uit as follows:

$$ \frac{{\partial {\varvec{X}}_{i}^{t} }}{\partial t} = {\varvec{U}}_{i}^{t} $$
(1)

The position Xi in the next time step is calculated using the Euler explicit method as follows:

$$ {\varvec{X}}_{i}^{t + 1} = {\varvec{X}}_{i}^{t} + {\varvec{U}}_{i}^{t} \Delta t $$
(2)

In the above, Δt is the time step. The oil particle movement is only considered in two dimensions on the sea surface (i.e., not three dimensions). The oil particle movement is assumed to follow the currents on the sea surface. The currents are assumed to be such that a vector synthesis can be calculated from each current component as follows:

$$ {\varvec{U}}_{i} = {\varvec{U}}_{oi} + {\varvec{U}}_{ti} + {\varvec{U}}_{wi} + {\varvec{U}}_{si} + {\varvec{U}}_{di} + {\varvec{U}}_{bi} $$
(3)

Here, Uoi is the advection velocity owing to the ocean current, Uti is the advection velocity owing to the tidal current, Uwi is the advection velocity owing to the wind-induced current, Usi is the mechanical spreading velocity, Udi is the diffusion velocity, and Ubi is a compulsory current vector dependent on the distance from the coastline boundary (this component is calculated as the distance between the particle and coast line boundary). Each velocity estimation method is explained below.

2.2 Advection Forces

We consider that the ocean and tidal current velocities are equal to the oil movement velocity. The calculation methods for wind-induced currents seem to follow two patterns. One is the “wind coefficient method” and the other is a direct wind-induced current simulation using a three-dimensional hydrodynamic model. In our previous study, we confirmed that the former method is suitable for calculating wind-induced oil advection [2]. In addition, the wind coefficient method has been used in many spilled oil transport simulation models (Table 1 in [2]). The wind coefficient method is briefly explained as follows. From the equilibrium of the tangential stress τ between air to water and water to air, the relationship between the wind at just the sea surface W and wind-induced current at the sea surface Uw is as follows:

$$ \tau = \rho_{a} C_{da} W^{2} = \rho_{w} C_{dw} U_{w}^{2} $$
(4)
Table 1 Database construction status of advection external force (as of January 2023)
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In the above, ρa and ρw are the densities of air and water, respectively, and Cda and Cdw are the drag coefficients of air to water and water to air, respectively. We assume that Cda and Cdw are equal, and the wind-induced current at the sea surface Uw is written as follows:

$$ U_{w} = \sqrt {\frac{{\rho_{a} }}{{\rho_{w} }}} W \approx 0.035W $$
(5)

In OILPARI, the oil particle movement velocity owing to the wind Uwi is calculated as follows:

$$ {\varvec{U}}_{wi} = C_{w} {\varvec{W}}_{10i} $$
(6)

Here, Cw is the wind coefficient and W10i is the wind velocity at 10 m from the sea surface at the position of the oil particle i. The wind velocity at 10 m from sea surface is larger than that at just the sea surface; thus, 0.03 is used for Cw in OILPARI. It is smaller than the 0.035 in the above Eq. (5), and the past study almost adopted 0.03 as the wind coefficient (Table 1 in [2]).

Among the advective external forces, the datasets for ocean currents and wind are constructed as shown in Table 1. The tidal currents in major inner bays (Tokyo Bay, Ise Bay, Seto Inland Sea) are calculated with a 270-m grid using the three-dimensional hydrodynamic model [4]. The tidal currents at the calculation time are calculated using a harmonic analysis. The tidal currents in the other inner bays and ocean area at the calculation time are calculated using the harmonic constant [5]. The calculation range is the same as the range of the dataset, i.e., 22.4–47.6 degrees north latitude and 120 degrees to 150 degrees east longitude.

2.3 Mechanical Spreading

We developed a model for the mechanical spreading of oil [6] as follows:

$$ {\varvec{U}}_{si} = k_{3m} \sigma_{n}^{1/2} t_{i}^{1/4} \Delta t^{ - 1/2} \left[ {\begin{array}{*{20}c} {\cos \left( {2\pi R_{{{\text{rand}}}} } \right)} \\ {\sin \left( {2\pi R_{{{\text{rand}}}} } \right)} \\ \end{array} } \right] $$
(7)

Here, k3m is the spreading model coefficient and is equal to 0.554 (N−1/2 m3/2 s−3/4). It is calculated based on a comparison between the model [7] and experiments [6]. σn is the net surface tension coefficient and ti is the elapsed time from the input of particle i. Equation (7) is a model for quick calculation; we are also developing a repulsive force model for calculating the details of mechanical oil spreading [2].

2.4 Oil Diffusion: Turbulent Diffusion

The oil diffusion is used to simulate the oil movement according to the sub-grid-scale currents. In OILPARI, the oil diffusion is calculated using a random walk technique.

$$ {\varvec{U}}_{di} = \sqrt {\frac{{2D_{H} }}{\Delta t}} \left[ {\begin{array}{*{20}c} {R_{n1} } \\ {R_{n2} } \\ \end{array} } \right] $$
(8)

In the above, DH is a horizontal turbulent diffusion coefficient (m2/s), and Rn1 and Rn2 are normal random numbers with an average equaling 0 and variance of 1.0. DH is typically in the range of 1–100 m2/s [8]. We previously provided a procedure for predicting DH and verified it using numerical simulations [9].

3 OILPARI Simulation System

3.1 sa-OILPARI

sa-OILPARI is an already developed system [3]; however, as the ocean current and wind datasets have been improved to high-resolution datasets by the JMA (Table 1), sa-OILPARI must be improved to accommodate them. As another improvement, a past analysis mode is added to understand the oil transport trends according to the season and sea area and to perform calculations to reproduce past oil spill incidents. In other words, it is possible to extract the initial values of the datasets shown in Table 1 (analytical values obtained by fusing the observed values with the data assimilation system) and to perform oil transport simulations using only plausible ocean current and wind datasets.

3.2 net-OILPARI

Overview

net-OILPARI is a web-based application for simulating real-time oil transport; it was officially launched in April 2022. One of its significant features is that users can access all of the functionalities without needing any special software; they only need to access the URL from their browser. The application provides an intuitive single-page graphical user interface (GUI, Fig. 1).

Fig. 1
A screenshot of a web based application titled net OIL P A R I for simulating realtime oil transport. On the left panel, there are 14 options. On the right panel, there is a map of Japan. A shaded square box in the bottom center is highlighted.

Screenshot of net-OILPARI

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Main Functions

net-OILPARI offers a range of functions, including server options, simulation options, history, a dashboard, report printouts, import simulation results, import local files, geographic information system (GIS) information, and online tutorials. Users can choose from various server options including meteorological and hydrographic databases. They can also select time-forward and time-reverse simulation options. The history function allows users to review past simulations, whereas the dashboard provides meters indicating the oil drift velocity, wind, current, wave height, and other relevant information. The report printout function enables users to print simulation reports, whereas the import simulation results function allows them to view the simulation results. Users can also import their geoJSON files into the map view, and the application can superimpose the GIS information such as the shoreline Environmental Sensitivity Index.

Implementation

net-OILPARI employs a server-client system with HTTP communication. The server-side consists of multiple back-end servers connected via HTTP (Fig. 2) to ensure flexibility and scalability. Each back-end server provides an application program interface according to its functionality; these servers are denoted as application, cronClient, engine, gpv_grib2, gpv_tide, shoreline, GIS, and watchdog (Table 2). These servers work independently and synchronously. They are all implemented with JavaScript (node.js) and JSON is used as the data format for the inter-server communication. Although JavaScript is not usually used for numerical simulations, it is used here because writing everything in one language assures good development and maintainability. The slow computation speed is solved by incorporating multi-threading techniques, especially in the engine server, where there are sub-servers called “cylinders” for calculating the drifts of particle subsets. These sub-servers can be located on the same computer or different computers, providing excellent horizontal scalability.

Fig. 2
A flow diagram. The browser leads to applications that connect the engine server and the data server. The data server connects G R I B 2 server. The watchdog interconnects the data server and application.

Topological schematic of net-OILPARI server system

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Table 2 Servers in the net-OILPARI
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4 Application for Marine Disaster Incidents

4.1 Oil Transport Simulation for Oil Spill Incident at Hachinohe Port

OILPARIs have been applied to many past oil spill incidents [3]. Since that report, the OILPARI simulations have continued. This section reports the results from a sa-OILPARI simulation of an oil spill from a ship that occurred in August 2021.

Materials and Methods for Oil Transport Simulation

A forecast simulation was conducted using sa-OILPARI on the oil spill incident from the woodchip carrier “CRIMSON POLARIS” that occurred off the coast of Hachinohe, Japan. The calculation conditions were as follows. The “OCN GPV” and “MSM GPV” datasets listed in Table 1 were used for the ocean currents and wind, respectively. The tidal current was calculated using a harmonic constant [5]. As with many oil spill incidents by ships, the spill conditions for this oil spill were not well known. Thus, the calculation conditions used in the model for the oil transport simulation were assumed as shown in Table 3. The oil spill site and time were set based on information from an automatic identification system and Japan Coast Guard. An oil particle was input at 86.4 s in each simulation. The volume of the particle was not considered because amount of spilled oil was unknown (i.e., the mechanical oil spreading by Eq. (8) was not considered).

Table 3 Simulation conditions
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Results and Discussion for Oil Transport Simulation

The spilled oil drifted to the northwest and beached the coast line around this area. The simulation results shown in Fig. 3 were qualitatively consistent with the actual situation. This simulation was conducted immediately after the notification of the incident, and the simulation results were provided to the concerned parties.

Fig. 3
3 maps of the shore of Okinawa Island, Japan, represent the increasing rate of oil spilling on the sea at 6, 12, and 18 hours. At 18 hours, higher breached oil at the shore is observed.

Simulation results of oil transport by sa-OILPARI. Blue particles denote spilled oil, red particles in (c) denote beached oil, purple vectors denote oil transport velocity by advection forces, and red squares denote the calculation area, respectively

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4.2 Pumice Transport Simulation in Pacific Ocean

The submarine volcanic eruption of Fukutoku-Okanoba in the Pacific Ocean in 2021 resulted in a significant amount of pumice (floating stone) washing up on the shores of Okinawa Island, Japan. As a result, the inflow of pumice into Tokyo Bay has the potential for a tremendous impact on Japan's economy. The MLIT needed to be alerted to the inflow of pumice into Tokyo Bay, prompting us to provide simulation.

Materials and Methods for Pumice Transport Simulation

In this case, we set two warning lines at the entrance to the bay mouth and used net-OILPARI to simulate the drift of pumice from these lines over the next 24 h. The prediction calculations were performed automatically and daily and were uploaded to the net-OILPARI server, enabling the corresponding institutions to view and download the results. The simulation conditions for advection terms were the same as those described in Sect. 4.1. This simulation was conducted as part of an emergency response to a crisis, so it did not involve detailed tuning of the pumice stone drift parameters. In other words, the wind coefficient was set to 3% (the same as in the oil transport simulation).

Results and Discussion for Pumice Transport Simulation

The simulation provides an approximate picture of the pumice drift prediction (Fig. 4). The gray particles drifted to south and did not drift into Tokyo Bay. This simulation results did not compare with the actual observed distribution of the pumice; however, no reports have shown large amounts of pumice intruding into Tokyo Bay. Accordingly, this calculation is judged to be qualitatively valid. This simulation can be used to establish an operational schedule for alert vessels. The micro-simulations conducted in this study to predict the possibility of pumice hypothetically existing at the mouth of the bay (flowing into the bay) also provide important knowledge for crisis responses. While macro-simulations of the drift of pumice from Okinawa to the vicinity of Tokyo Bay are important, this study's micro-simulations offer valuable insights into the behaviors of the pumice in the bay mouth, aiding in crisis response efforts.

Fig. 4
A screenshot of a web based application titled net OIL P A R I for simulating realtime oil transport. On the left panel, there are 14 options with 3 radar charts below for oil drift, wind, and ocean and tidal current. Right, there is a map of Japan. A shaded rectangular box highlights Tokyo Bay.

Pumice drift simulation by net-OILPARI. Red particles indicate the positions predicted at the time set by the time slide bar. Gray particles show the trajectory of pumice over 24 h. Red rectangle shows the Tokyo Bay area

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5 Conclusions

This paper discussed the improvements to and development statuses of OILPARIs. We recognize that additional improvements are necessary in the future, as follows.

As the wind and current datasets are expected to be improved, the OILPARIs must be adjusted to compensate for format-changing input datasets from time to time. As a concrete plan, from March 14, 2023, the resolution of the JMA GSM GPV data has been improved to 0.1 degrees latitude and 0.125 degrees longitude. Thus, the program should be modified in the near future.

As the influence of the freshwater inflow is relatively strong in coastal areas compared to the open ocean, it is necessary to construct a flow simulation system able to consider rivers and precipitation. We are conducting research on the construction of a simulation system for coastal flow forecasting using an ecological hydrodynamic simulation system [10], and we would like to work on the cooperation between OILPARI and the flow simulation system in the future. Similarly, it is possible to improve the accuracy of the oil transport simulation by using high-resolution wind velocity [11, 12].

OILPARI only simulates transportation and does not simulate the ultimate fate of the oil (e.g., emulsification, evaporation). Thus, constructing a fate/weathering simulation system is also required for effective oil pollution countermeasures. One popular target model is the “Automated Data Inquiry for Oil Spills” model developed by the National Oceanic and Atmospheric Administration (NOAA)) and operated as part of the General NOAA Operational Modeling Environment suite.

net-OILPARI is an advanced web-based application that allows users to simulate real-time oil transport. Its intuitive single-page GUI interface, coupled with its range of functions and scalability, makes it an excellent tool for oil spill response and management.