Keywords

1 Introduction

In recent years, the urbanization and development of new infrastructure increased the demand for sand by threefold, and as per United Nations, the global annual demand for sand is 50 billion tons [1]. Sand is needed for land reclamation and beach nourishment in coastal regions for the expansion of land and replenishment of eroding coastlines and often acquired from borrow pits dredged in the shelf and offshore regions [2]. Dredging in the offshore region often leaves borrow pits that are substantially different from the pre-dredging and neighboring environment [3]. Dredging of borrow pit can contribute to physical changes by altering the density stratification of water column within the borrow pits and restricting the vertical mixing. In Japan, extensive dredging projects were executed particularly for reclaimed lands as Japan has one of the longest coastline, ranked 6th in the world and major economic centers are located along the coastal areas. There was a paramount development contribution to the economy by Japanese ports and harbors, leading to sand requirements for construction and landfilling projects [4]. There are many dredged depressions in Osaka Bay, which is a subject study area in this research. From the 1960s to 1970s, Osaka Bay also had several reclamation projects for industrial purposes and sand was mined from coastal regions which left several dredged depressions with stagnant water leading to a higher occurrence of blue tides [5]. An experiment was conducted in Osaka Bay to assess the sediment quality in borrow pits and it was found that the sediments in borrow pits are highly contaminated and the oxygen consumption in borrow pits was 2–10 times that of outside neighboring sediments [6]. It is somewhat challenging to reproduce the hydrodynamic conditions in borrow pits due to the limitation of borrow pit size. Hence, a state-of-the-art modeling framework is required that has the capability of conducting high-resolution simulations. In this study, a non-hydrostatic 3-D hydrodynamic model is used to accurately reproduce the hydrodynamics on coarse and high-resolution mesh configurations. This modeling framework can locally modify the uniform Cartesian mesh system to a certain area of interest.

2 Methodology

2.1 Study Area

Osaka Bay as shown in Fig. 1 is located in the western part of Japan almost in the middle of the main island. It is the eastern part of the mighty Seto Inland Sea. The Seto Inland Sea is the biggest semi-enclosed coastal sea with over 700 small islands. It is stretched over a length of 500 km with an average water depth of 30 m [7]. Osaka Bay has an oval shape and it runs over 60 km with a 30 km width and an average water depth of 28 m. A strait called Akashi Strait which is situated between the Japanese islands of Honshu and Awaji has a width of 4 km connects Osaka Bay at the western end with the neighboring areas of Seto Inland Sea, while on the southern side, the other Kitan Strait with a width of 10 km connects it to the Kii Channel which is further connected to the Pacific Ocean.

Fig. 1
A map of Osaka Bay, Japan. The labeled areas are the Himeji boundary, Akashi Strait, Kitan Strait, Wakayama Boundary, Naruto Strait, and Kii Channel. On the bottom right, there is a map of Japan highlighting Osaka Bay with a shaded box.

Study area map of Osaka Bay, where hollow circles represent the locations of observation stations and dotted lines are representing open boundaries

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2.2 Study Area

A 3-D non-hydrostatic model called “EcoPARI” [8] was employed to simulate the coarse and high-resolution hydrodynamic conditions of Osaka Bay. In the past, this model was utilized to successfully simulate the hydrodynamics and ecosystem variables for different study sites in Japan [9,10,11]. The hydrodynamic model is primarily comprised of a basic continuity equation, momentum equations, sea state equation, and scalar transport equations. Turbulent kinematic viscosity and eddy diffusivity in the horizontal direction (XY Plain) employed a large eddy simulation (LES) model, while in the vertical direction (Z, Plain) an upgraded turbulent diffusion approach model was used [12].

EcoPARI meshes the geometry through a uniform Cartesian grid system. This mesh system has a limitation in the case of high-resolution simulations as it will become computationally too expensive. To counter this issue, two-dimensional building cube method (hereafter BCM) was introduced in the EcoPARI, which can increase grid resolution level by level by subdividing into child cubes via insertion of root cubes using a quadtree structure. This BCM was originally proposed by Nakahashi, and since then, it has been successfully used in several computational fluid dynamics applications [13]. A typical example is shown in Fig. 2; an adaptive mesh refinement can be seen around a borrow pit through BCM. In a quadtree structure, the parent or root cube contains the average data of four child cubes, and deeper traversing in the tree will yield more detailed and precise results. Level 1 has further refined mesh size as compared to level 0, and similarly, all the nodes in level 1 have a further 4 nodes as shown by level 2. Hence, by increasing the layers of the quadtree structure, the levels can be increased so does the mesh size. BCM applies the governing equations that describe the physical phenomena being simulated to each cell within the mesh. These equations pertain to fluid dynamics, heat transfer, or other physical processes. In case of EcoPARI, it employs finite difference method to discretize the governing equations within each cell. These methods approximate derivatives and integrals in the equations. The numerical solutions are computed iteratively over the entire mesh. The solution process is iterative, where the values are repeatedly updated until the solution converges to a stable state or meets a specific convergence criterion.

Fig. 2
A diagram of the grid is on the left, in which a single cell is labeled level 0, a cell divided into 4 parts is labeled level 1, and another cell divided into multiple parts is labeled level 2. The right side has a node diagram. A node at level 0 is split into 4 nodes at level 1, from which a node splits into 4 nodes at level 2.

A typical example of BCM, where a quadtree layered structure is dividing the root cubes into four child cubes

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2.3 Numerical Experiments

The first numerical experiment comprised of low-resolution hydrodynamic simulation covering the entire model domain while in the second numerical experiment, BCM was employed in the borrow pit region to reproduce the detailed high-resolution hydrodynamics. The objectives are devised by keeping the size of the borrow pit under consideration as 100 m mesh was able to trace the shape and bathymetry while a low-resolution (800 m) bathymetric map was unable to replicate the actual geometric and bathymetric conditions. As shown in Fig. 3, the shape and bathymetry of the borrow pit are also very different in both coarse and high-resolution maps. In the case of 800 m grid configuration, the borrow pit is only represented by a few grids and it looks rectangular in shape while in the case of 100 m mesh configuration, it is represented by several grids and it signifies the actual field conditions.

Fig. 3
A heat map of a borrow pit depicts the distribution of depth. The depth is highest in the middle area and moderate in the nearby area. The right side depicts a close up view of the depth distribution in the heat map.

Zoomed borrow pit bathymetry; (a) is demonstrating the shape of the borrow pit under 800 mesh configuration. While subplot (b) is displaying the detailed borrow pit bathymetry and shape under 100 m mesh configuration

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3 Results and Discussions

The coarse-resolution simulation model was evaluated by comparing its results with observed data from monitoring stations, and regression results are shown in the following table. The "B-3" station near a major river mouth showed anticipation of surface salinity but had higher fluctuations and the highest RMSE. Surface temperature was well captured with high R2 and low RMSE. Bottom salinity was overestimated at “B-3” during summer months. The “A-2” station showed similar performance, but with improved surface salinity. The "A-6" station had the smallest RMSE for bottom salinity and temperature. "A-10" had less surface salinity fluctuation. The “A-11” station near the bay mouth showed good reproducibility of water temperature and salinity. Overall, the model's performance varied among stations, with varying levels of agreement with observed data (Table 1).

Table 1 Assessment of coarse-resolution simulation on different spatially distributed stations of varying depth. A regression analysis was conducted for water temperature and salinity from the beginning of January 2015 to the end of December 2015
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Figure 4 represents the time series comparison of both simulations with observation and subplot “a” is showing the comparison of the “B-5” station while subplot “b” is showing the comparison of the “B-P” station. The major discrepancy was found in high-resolution simulation in the surface layer, and sometimes model was unable to reproduce the surface salinity and temperature, especially in August. During this period, the surface salinity was overestimated while the surface temperature was underestimated. As reflected by the observed data, the warm fresh water on the surface might be coming from the major rivers located in the proximity of the borrow pit, and in high-resolution simulation, this warm freshwater was pushed away from the borrow pit. Contrary to high-resolution simulation, the coarse-resolution simulation was able to capture this trend. However, the high-resolution simulation results were promising in the lower layer; especially in the summer season, the bottom water temperature and salinity were well reproduced as compared to coarse-resolution simulation.

Fig. 4
8 line graphs of temperature and salinity versus different date labeled location B 5 and B p for surface and for bottom represent 2 fluctuating lines for simulated salinity B C M 100 m, simulated salinity 800 m, along with 2 dots and 2 lines for observed salinity and observed temperature.

Time-series comparison of salinity and temperature between coarse and high-resolution simulations

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To see the spatial comparison, a cross-sectional distribution of hydrodynamic parameters was also plotted for a particular date as shown in Fig. 5; it was the time when bottom water temperature and salinity within the borrow pit showed larger discrepancy between coarse-resolution and BCM simulation. This discrepant period is shown in Fig. 4(b). It was evident from the results that in case of coarse-resolution simulation a thick warm freshwater layer existed in the surface while in case of BCM it was rather thin. Furthermore, for the bottom layer, coarse resolution showed existence of denser water as compared to BCM simulation. During this particular time step, the BCM results were in good agreement with observation as compared to coarse-resolution simulation. Apart from that, the flow magnitude was also different between both simulations and a detailed flow field was obtained within the borrow pit.

Fig. 5
4 heat maps represent the distribution of salinity and temperature in a borrow pit, with arrows representing the direction at different times. The temperature is highest, and salinity is lower at the top layers.

Instantaneous cross-sectional comparison of borrow pit for 1st of August. The upper 1st and 2nd subplots are showing the salinity and temperature for 800 m simulation while lower two subplots are showing the same parameters for BCM simulation. Furthermore, quivers are depicting the flow magnitude and direction

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Despite facing some discrepancies in high-resolution simulation, it is still indispensable to use the 100 m bathymetric map to trace the actual borrow pit shape and bathymetry. BCM resolved this issue by multilevel simulation with overall coarse-resolution simulation over a major part of the model domain while the high-resolution simulation only in the borrow pit region. To compare the calculation cost, both coarse and high-resolution (BCM) simulations were conducted on the same supercomputer (Oakbridge-cx) having a CPU clock frequency of 2.70 GHz. In case of low resolution simulation, the model has the freedom to choose the computational resources (number of cores) for parallel computations depending upon the distribution of grids in both “X” and “Y” directions, while in the case of BCM simulation the grid distribution system is autonomous and the model automatically selects the number of cores from given computational resources. Hence, a fixed 130 cores were utilized for coarse-resolution simulation to simulate one full year, i.e., 2015, while in the case of BCM 112 cores were automatically allocated to execute the same simulation period. In the case of coarse resolution, the simulation was completed in 4.35 h while the BCM simulation was completed in 11.00 h. The BCM simulation execution time was 2.50 times as compared to coarse-resolution simulation, but still, it was quite fast. Furthermore, practically, it will be computationally too expensive to simulate the entire model domain with just a 100 m mesh configuration, which has a 64 times greater number of grids as compared to an 800 m bathymetric map. The BCM simulation reasonably worked twofold by reducing the computational cost and increasing the model resolution.

4 Conclusion

In this study, a 3-D non-hydrostatic hydrodynamic model with the inclusion of BCM was successfully employed to accurately reproduce the spatial hydrodynamics on a high-resolution mesh configuration. The purpose of BCM was to locally modify the Cartesian mesh configuration from coarse resolution to high resolution to get the detailed hydrodynamic conditions, especially in the bottom layer of a borrow pit. The high-resolution simulation results were promising in the bottom layer; especially in the summer season, the bottom water temperature and salinity were well reproduced as compared to coarse-resolution simulation.