FVCOM was applied to obtain the hydrodynamic field in this study. The hydrodynamic equations were numerically resolved on unstructured grids using the finite-volume method. Because of the advantage of the body-fitted grid, FVCOM is widely used in estuarine and coastal areas. In addition, the finite-volume algorithm guarantees volume and mass conservation of the momentum fluxes. The reader is referred to Chen et al. (2003) for further details on the governing equations.

In this study, the model area is located 111.86°–112.97° E, 21.45°–22.02° N ( Figure 1 ), which comprised 4,505 nodes and 8,172 triangles (elements) with 200 m minimum horizontal grid resolution and five uniform σ layers. Horizontal diffusion was parameterized based on Smagorinsky’s formation, and vertical turbulent mixing was calculated with the 2.5-level Mellor and Yamada turbulence model. The tide level data on the boundary were taken from the TMD toolbox (Tidal Model Driver) (Padman, 2005) with the TPXO7 global tide model, which included eight tidal constituents (M₂, S₂, K₁, O₁, P₁, Q₁, N₂, and K₂). The sea surface wind data were extracted from the ERA5 (European Centre for Medium-Range Weather Forecasts) reanalysis dataset. The drainage water of the NPCS was also included in the model, with the flux set as 350 m³/s (Chen et al., 2013) at a temperature of 8°C higher than natural environment seawater.

FVCOM produced a three-dimensional hydrodynamic field hourly. Subsequently, the surface current field was extracted and interpolated to drive a particle tracking model to simulate the drifting process of Acetes, which was then used in the construction of the LFN.

The network, also called the graph in mathematics, is a set of points joined together in pairs by lines. The points are referred to as vertices or nodes and the lines referred to as edges or links. Many objects of interest in the physical, biological, and social sciences can be considered as networks (Newman, 2010). The adjacency matrix is the most common representation of a network. The adjacency matrix A is the matrix with elements A _{i j} :

The network constructed by A _{i j} is unweighted. Similarly, the weight matrix representing the strength of the connection between vertices i and j is denoted as W _{i j} :

In the ocean, one way to establish the network is to base it on the particle transport dynamics, in which the nodes correspond to discretized domains and the links are defined by the connectivity between the regions (Ser-Giacomi et al., 2015a). The research domain was divided into 831 sub-regions ( Figure 2 ) with an area of 4 km². A total of 250,000 particles were seeded in the domain, and all particles were tracked from time t ₀ March 1) to time t (March 30). The swimming speed of Acetes was far less than the flow velocity, so that they are considered as being passively advected by the sea current:

where x   → is the displacement vector of the particles at time t and d x → d t   the derivative of the displacement vector x → to time t. The v   → is the velocity of the particle coming from the FVCOM output.

For any particle that moves from V _i to V _j , the connection from V _i to V _j is established defining the edge E _{i j} (A_ij = 1). However, it should be emphasized that the link in the network is directed, which means that the link from V _i to V _j is not the same as that from V _j to V _i . Moreover, the weight of the links is defined by the transport probability of particles from vertex V _i to V _j :

where N _{i j} is the number of particles from V _i to V _j and N _i is the initial number of particles in V _i . P _{i j} (t ₀,τ) is regarded as the weight of the link from node V _i to node V _j . Subsequently, the network described by a transport matrix P(t ₀,τ) as constructed.

Figure 5 depicts the flow field distribution at ebb time and flood time during the spring tide in the simulated area. At flood time, the current flowed from the southeast to northwest, and at ebb time, the flow direction is in reverse. During flood time, the flow velocity in the whole field was mostly at 0–0.4 m/s, which can reach 0.4–0.8 m/s in the area around the NPCS and Xiachuan Island due to the influence of topography. The velocity during the ebb time was lower than that during flood time.

To clearly describe the transport and distribution of Acetes near the nuclear power plant, this study utilized a Lagrangian particle tracking model using passive particles to represent the Acetes. The particles were seeded in a uniform distance of 200 m and ran for 30 days, with March 1, 2020, as the initial release moment. Figure 6 shows the distribution of the particles for 3, 7, 15, and 30 days after releasing the particles.

The particles were mainly transported offshore for 3 days in the study area. After 7 days, the particles started showing a spatial dispersion near the coast, with some striped distribution structures. Figures 6C, D indicate obvious strips of structures where the aggregation of the particles occurred near the sea entry of three rivers. In contrast, the particles at the estuary spread rapidly, and the number of remaining particles was very small. The particles were mostly in patched aggregates near several islands on the eastern side of the study area. Since Acetes are poor swimmers and can be considered as plankton whose transport and distribution are controlled by currents, the particle tracking results can represent their trajectories in this region.

The degree of a vertex in a graph is the number of edges connected to it. In a directed network, the connectivity of each vertex is described by both the in-degree and the out-degree. The in-degree k i in of vertex i is the number of edges arriving at i while the out-degree k i out of vertex i is the number of outgoing edges from i. In terms of the adjacency matrix A _{j i} the in-degree and out-degree can be written as:

The degree of a vertex has an immediate interpretation considering centrality, quantifying how well an element is connected to the other elements in the graph (Barrat et al.). Regarding the LFN that corresponds to the aggregation and diffusion of materials in the ocean, the vertex with a large in-degree implies that the material easily accumulates there, which is generally considered as a “sink” in the description of ocean material transport; in contrast, a large out-degree indicates that the vertex can be considered as a “source”.

Figure 7 illustrates the distribution of the in-degree and out-degree within 30 days. The degrees were mostly less than 10, and vertices with a large degree are likely to be near the coast. Figure 7 also highlights that the in-degree and out-degree were higher at offshore areas, i.e., sea areas where the cooling system is located that act both as a “sink” and as a “source” of the materials around them. From a network’s perspective, it is the hub vertex in the material transport process. If any environmental variations influence the nearby material transport, for instance, reducing the diffusion process, the materials will be continuously convected inwards because of the large in-degree, but not outwards due to the limited diffusion process. The NPCS is in an unstable equilibrium condition, and this material transport pattern brings with it a high risk of natural outbreak of these organisms.

A path in a network is any sequence of vertices so that every consecutive pair of vertices in the sequence is connected by an edge in the network (Newman, 2010). The path is often used to analyze the connectivity among vertices, and the path concept depends on the distances among vertices. In the ocean, the distance is not limited to the Euclidean distance, as the shortest time to the fastest path or the most probable path (MPP) is more meaningful in practice. This study applied the MPP to determine the optimum path.

When all paths connected to the location of the nuclear power plant were found, we collected their starting points and labeled them as the source of Acetes (red dots in Figure 8 ). Obviously, the results depend on the integration time. Considering the results within 30 and 90 days, the potential source area was located east of the nuclear power plant, which covered an area of about 120 km², and within 90 days, the area was about 475 km².

In order to determine the path, we introduced another network metric, the betweenness centrality. Betweenness measures the extent to which a vertex lies on the key paths between other vertices. Mathematically, if N _{j l} s the total number of the MPPs (Ser-Giacomi et al., 2015b) from V _j o V _l and N _{j l} (i) is the number of these MPPs that pass through the V _i the betweenness of V _i is defined as:

Vertices with high betweenness pose a greater influence within a network. On the other hand, in terms of the ocean, betweenness is a measure of the hidden bottlenecks of the material transport system, and aligned high-betweenness vertices indicate the major material transport pathways (Ser-Giacomi et al., 2021). Hence, the betweenness is critical in the analysis of material transport and in the determination of the ocean’s flow structure.

As mentioned above, the Acetes near the nuclear power plant originated from the east with a large probability. The betweenness results showed that the organisms were not uniformly or randomly transported to the nuclear power plant’s sea area. Instead, two clear transport pathways ( Figure 9 ) passed through the sea area of the nuclear plant. The first pathway goes along the coast that extends to the eastern boundary of the research domain, while the other bypasses the southern edges of Xiachuan Island and merges with the first pathway just near the NPCS. The two pathways formed a “-<“-shaped transport structure, and the intersection of two major material transport pathways was only about 10 km from the NPCS. Most of the time, this “-<“-shaped pathway carries materials westward and works in balance. However, when any environmental interruptions such as coast-pointing winds occur, this fragile system falls into unbalance and the material flow is cut off, which might result in an organism aggregation or even in a harmful outbreak. The effect of wind direction will be discussed in the next section.

The distribution of Acetes is affected by biological, chemical, and physical factors, with their outbreak mechanism still being poorly understood. In this study, we focused on the dynamic factors. Figure 10 reveals the relationship between wind and the daily catch of Acetes from 2020 to 2021. The Acetes catch data were provided by the State Key Laboratory of Nuclear Power Safety Monitoring Technology and Equipment, and the wind data around the NPCS were extracted from the ERA5 reanalysis data. An Acetes outbreak is most likely to happen in late winter or in early spring, so we aimed to analyze and determine what happens during these periods. We hypothesized that the temperature and the material transport pattern are the intrinsic causes, and wind is an acceleration factor. Intriguingly, the outbreak of Acetes showed a strong relationship with the time when the winds are turning from northeast to southwest. Wind stress turning from offshore to onshore influenced the material transport pattern; that is, the two major pathways intersected in the cooling system, thus causing the aggregation of Acetes around it. Afterward, with the reversed wind direction, the old transport pattern was destructed and the seawater temperature also rose too high for Acetes to survive, explaining the reduction in the daily catch of Acetes.

Subsequently, we ran a parallel experiment that removed the surface wind on the ocean to clarify the model’s sensitivity to wind. The configurations of the hydrodynamic model and the network were the same, except for the removal of the surface wind stress. The two experiments were denoted as the “with-wind” case and the “no-wind” case.

On the one hand, Figure 11 depicts the betweenness pathways in the no-wind experiment, where the shape of the pathways was similar to that in the with-wind experiment, which is a two-pathway flow from the east to the west conjunct in the middle; however, the pathways in the no-wind experiment were shifted two or three grids to the south and thus staggered the NPCS. Most materials transported westward will not go through the NPCS, if the wind is weak. Therefore, the Acetes had a small probability of touching the NPCS or even break out without the assistance of the northwestward winds.

On the other hand, the in-degree and out-degree of the network, which depict the characteristic of the aggregation and diffusion processes of Acetes, also made significant changes under the influence of wind. When wind was added to the model, the in-degree, which represents the sink of a material, increased significantly ( Figures 12A, B ). However, the out-degree, which represents the source of the material, decreased by about 50% when wind was included ( Figures 12C, D ). To sum up, the extra northwestward wind increased the extent of the material sink and decreased the extent of the material source near the NPCS.