Feasibility of tide simulation using nesting module of FVCOM—a case study of Xiangshan Bay

The nesting module of FVCOM is widely utilized in numerical simulations for both nearshore and offshore. However, the details of the nesting module on computation accuracy and efficiency have not been quantitatively assessed. In this study, we take Xiangshan Bay as a case study area and design two groups of experiments to examine this issue on tide simulation. The results indicate that nesting module effectively incorporates all tidal information from the open ocean through the boundary. The nesting module experiment successfully simulates the tides almost exactly similar to the original tides, while achieving an efficiency improvement of approximately 48% by avoiding computations outside the high-resolution area.


Introduction
The ocean plays an important role in maintaining global climate balance, and studying it is crucial for humanity's sustainable development.Study on the ocean has two main aspects: study on the open ocean and coastal areas.Both aspects of study are extremely important, especially as coastal ocean processes directly affect local economy and environment.
Numerous studies primarily focus on either nearshore or offshore areas, while often fail to adequately consider the offshore's impact on the nearshore.FVCOM (Finite Volume Community Ocean Model) is a three-dimensional hydrodynamic model using unstructured mesh.It is widely used in ocean study from global to local scales because its flexible spatial resolution [1] .The nesting module of FVCOM can proficiently integrate large-scale models with small-scale models.When studying the complex coastal areas, this module helps in detailed modeling of specific regions while also considering the influence of the open ocean.Prakash A [2] used nesting module to build a high-resolution unstructured grid 3-D ocean-sea ice-ice shelf for numerical investigations of the Petermann ice shelf and fjord.Ge J [3] used nesting module to establish a the East China Sea and Changjiang Estuary (ECS -CE) system with the aim at resolving coastal ocean dynamics and understanding different physical processes.Wei E [4] used nesting module to develop two FVCOM-based, high-resolution, estuary-scale nested forecast models for the northwest and northeast Gulf of Mexico, respectively.
However, the details of the nesting module on computation accuracy and efficiency have not been quantitatively assessed.Therefore, we take Xiangshan Bay as a case study area and design two groups of experiments based on FVCOM to evaluate the details of the nesting module on computation accuracy and efficiency.

Study Area
Xiangshan Bay is located in the coastal area in the eastern Zhejiang Province, China(figure 1).It is bordered to the north by Hangzhou Bay, to the south by Sanmen Bay, and to the east by the Zhoushan Islands.Xiangshan Bay is a narrow, semi-enclosed and deep-water bay, with rich fishery resources and developed aquaculture.

Design of Experiments
In this study, two groups of experiments are designed based on FVCOM to evaluate the stability and accuracy of nesting module.Both of the two experiments consist of three sets of grids (figure 2).Due to M2 is the major tidal constituent in Xiangshan Bay, Experiment Group A only includes the M2 tidal constituent, while Experiment Group B includes eight tidal constituents (M2, S2, K1, O1, N2, K2, P1, Q1) and two shallow-water constituents (M4, MS4).The specific experimental details and parameters can be found in Table 1.Case A1 and Case B1 are large-scale grids, with lower resolution within Xiangshan Bay, and their boundaries are provided by the TPXO9 model [5] ; Case A2 and Case B2 are also large-scale grids, while with higher resolution within Xiangshan Bay, and their boundaries are provided by the TPXO9 model as well; Case A3 and Case B3 are high-resolution grids specific to Xiangshan Bay, and their boundaries are forced using the nesting boundaries calculated from case A1 and case B1, respectively.

Data Source and Analysis Method
To enhance the accuracy of simulating hydrodynamics in both the open ocean and nearshore, the bathymetric data utilized in all experiments are digitized results derived from electronic nautical charts.Additionally, the coastline data is sourced from high-resolution coastlines extracted from Google Maps.
The open-boundaries of Case A1, Case A2, Case B1, and Case B2 are forced by tidal elevations calculated using harmonic constants provided by the TPXO9 model: where is each tidal constituent, is the total number of tidal constituents.ℎ is the tidal elevation at time , h 0 is the residual water level, is the amplitude factors, is the angular speed, 0 + is the initial phase lag, while and are the amplitudes and phase lag which is relative to the Equilibrium Tide at Greenwich, respectively.
The correlation analysis in this study is conducted using the Pearson correlation coefficient [6] : where is the Pearson correlation coefficient, and are the ℎ observations of the two variables, and are the means of the two variables.

Results
Since previous studies have repeatedly verified the accuracy of the Xiangshan Bay model by comparing the modeled tidal elevation with the observed tidal elevation [7] , this paper will not elaborate on the model calibration and mainly focus on the comparison among experiments with and without the nesting module.
To visually demonstrate and quantify the details of the nesting module on tide simulation, this study selected station S (121.8°E,29.64°N) in the central of Xiangshan Bay and output its water elevation.Figure 3 shows the time series of simulated water elevation for station S in Case A1, Case A2, and Case A3.It can be observed that the model stabilizes after 10 days of calculation.The waveforms of Case A1, Case A2, and Case A3 are almost same, with only little differences in amplitude.Figure 4 shows the Taylor diagram based on the time series of water elevation for station S in Case A1, Case A2, and Case A3.Through correlation analysis, the correlation coefficient between Case A2 and Case A1 is as high as 0.99, and the correlation coefficient between Case A3 and Case A1 can also reach 0.94.The main difference between Case B3 and Case B1 is reflected in the amplitude at high tide, about 0.2m, while at low tide the difference is not significant.Overall, when considering only the M2 tidal constituent, the use of the nesting module has a minimal influence on simulation accuracy, and the differences in amplitude are slight.All experiments successfully simulate the tidal dynamics in the Bay.As an example, Figure 5 shows the distribution of surface tidal velocity in Case B1 at the flooding and ebbing time.It can be seen that the currents at the flooding and ebbing time are basically reversed, and the areas of maximum velocity are located in the middle of the inner Xiangshan Bay. Figure 6 shows the amplitude time series for station S in Case B1, Case B2, and Case B3.When considering multiple tidal constituents, the station exhibits a noticeable tidal asymmetric, which is similar to previous study [8] .Similar to Experiment Group A, the waveforms in Experiment Group B are nearly identical, with little differences in amplitude.Figure 7 shows the Taylor diagram based on the time series of water elevation for station S in Case B1, Case B2, and Case B3.Through correlation analysis, the correlation coefficient between Case B2 and Case B1 is as high as 0.99, and the correlation coefficient between Case B3 and Case B1 can reach 0.91.However, unlike Experiment Group A, the differences in amplitude between Case B3 and Case B1 are evident not only at high tide but also at low tide.Overall, the nesting module effectively incorporates all tidal information from the open ocean through the nesting boundary.Compared to the experiments running the entire large-scale model, the experiments running a small-scale model utilizing the nesting module have very little differences in simulated results.The differences in amplitude are slight, with the main differences occurring at high and low tides.Based on previous discussion, it is evident that the utilization of the nesting module does not exert a significant influence on the calculated tidal results.However, its effect on computational efficiency has not been quantified.Therefore, we use the Intel(R) Xeon(R) Silver 4214R CPU @ 2.40GHz with the same number of cores (48 cores) to statistically analyze the computational efficiency of the above experiments.The simulation duration for all model runs was set to one month, enabling a quantification of the influence of using the nesting module on computational efficiency.
The computation duration for each experiment is shown in Table 2.The difference in computation duration between Experiment Group A and Experiment Group B is minimal.Considering fluctuations in CPU calculations, it is evident that the tidal boundary components do not affect the simulation duration significantly.Taking Experiment Group A as an example, compared to Case A1, the computation duration of Case A2 is about 10% longer, attributed to its higher resolution within Xiangshan Bay and more computational grid nodes.However, the utilization of the nesting module in Case A3 demonstrates a notable enhancement in computational efficiency compared to Case A1, showcasing an increase of approximately 48%.The results indicate that the nesting module can significantly enhance computational efficiency while minimally affecting the calculation results.It would be efficient to firstly run a large-domain FVCOM model (for example, a global FVCOM model) and then set up boundaries to run multiple high-resolution small-domain coastal models.

Conclusions
In order to quantitatively evaluate the nesting module of FVCOM on computational accuracy and efficiency, we take Xiangshan Bay as a case study area and design Experiment Group A and Experiment Group B, corresponding to scenarios with solely the M2 tidal constituent and multiple tidal constituents, respectively.Within each experiment group, three sub-experiments were conducted: a low-resolution and large-scale grid driven by TPXO9, a high-resolution and large-scale grid driven by TPXO9, and a high-resolution Xiangshan Bay grid driven by nesting boundaries.The results are as follows: 1. Whether only considering the M2 tidal constituent, or considering eight major tidal constituents and two shallow water constituents, the nesting module of FVCOM effectively incorporates all tidal information from the open ocean through the nesting boundary.Compared to the experiments running the entire large-scale model, the experiments running the small-scale model used nesting module independently only have little differences in amplitude, with the main differences occurring at high and low tides.
2. The computation duration results for each experiment under the same hardware conditions shows that the nesting module significantly enhances computational efficiency, achieving an efficiency improvement of approximately 48% in this study by avoiding computations outside the high-resolution area.
However, the ocean comprises other important components, such as large-scale ocean currents.In this study, we specifically focused on assessing the influence of the nesting module on tidal calculations.The feasibility of this module on other components will be considered in future studies.

Figure 1 .
Figure 1.Location of Xiangshan Bay(Area marked by black box).

Figure 2 .
Figure 2. Grids of Xiangshan Bay ((a) Large-scale grids with lower resolution; (b) Large-scale grids with higher resolution; (c) High-resolution grids specific to Xiangshan Bay.The red line in the indicates the nesting boundary and the red dot indicates station S.)

Figure 3 .
Figure 3.The time series of water elevation for station S in Case A1, Case A2, and Case A3.

Figure 6 .
Figure 6.The time series of water elevation for station S in Case B1, Case B2, and Case B3.

Table 1 .
Experimental Descriptions and Parameters

Table 2 .
Computation Duration for Each Experiment under Similar Hardware Conditions