The Effect of Grid Resolution on Hydrodynamic Modeling Free

Hydrodynamic models use mathematical equations to describe the motion of fluid particles. The spatial domain of any hydrodynamic model is partitioned into cells or nodes using a grid. Bathymetry is interpolated to the grid to represent the volume of virtual fluid in any cell at any time. The fluid within the model is moved from cell to cell based on equations of motion and transport. These equations are solved for each cell at each time step.

Grid resolution is an essential aspect of any hydrodynamic model. Models with finer-resolution grids can represent the bathymetric surface and flow patterns with more detail. Models with finer-resolution grids also require more computational resources to run. Guidance determining optimal grid resolution is lacking, largely because it is dependent on the model, site, and application. Because of this, the determination of grid resolution in most hydrodynamic modeling studies is subjective.

Various studies have investigated the effect of grid resolution on hydrodynamic model results (Table 1). Studies have been conducted in different types of water bodies, including rivers (Bomers, Schielen, and Hulscher, 2019), river and floodplain systems (Altenau et al., 2017; Horritt and Bates, 2001; Jarihani et al., 2015), oceans (Putman and He, 2013), bays and gulfs (Andrejev et al., 2011; Bracco et al., 2016, 2018), and coral reefs (Colberg et al., 2020; Saint-Amand et al., 2023). These studies have investigated how grid resolution affects various model outputs, including temperature, salinity, water-surface elevation, flow, velocity, particle trajectories, and inundation area (Table 1). Of the 16 studies listed in Table 1, 13 concluded that finer grids produce more accurate simulations. Three of the studies concluded that grid resolution is conditionally significant in producing accurate simulations (Bomers et al., 2019; Horritt and Bates, 2001; Jarihani et al., 2015).

This study investigates the effect of grid resolution on the efficiency and accuracy of modeling water-surface elevation and salinity in Biscayne Bay, Florida, using a three-dimensional hydrodynamic model. The study' hypothesis is that increasing grid resolution will improve salinity and water-surface elevation results. The specific objectives of this study are as follows:

1. Develop five hydrodynamic models with varying grid resolutions: fine, medium, coarse1, coarse2, and coarse3;

2. Evaluate the accuracy of the models in simulating water-surface elevation and salinity by comparing the model outputs with observed data; and

3. Assess the effect of grid resolution on modeling water-surface elevation and salinity.

Biscayne Bay is located on the Atlantic Coast of South Florida, United States, at a latitude of 25°35′49.02″ N and a longitude of 80°15′50.58″ W; the bay is 97 km long, is up to 13 km wide, and has a surface area of 700 km² (Figure 1). Biscayne Bay is bordered by the Florida mainland on its western side, a swath of barrier islands to the north, a sizeable shoal to the east, and the northernmost Florida Keys to the south. A valuable economic resource for the region, Biscayne Bay provides opportunities for fishing, boating, and several other recreational activities. The area surrounding Biscayne Bay is also home to several parks and protected areas, including Biscayne National Park, which houses the largest marine parks in the National Park system (National Park Service, U.S. Department of the Interior, 2018).

Environmental Fluid Dynamics Code Plus (EFDC+), developed by Dynamic Solutions International, is a successor to the EFDC (DSI, LLC, 2023; Hamrick, 1992). Fundamental principles of the EFDC+ hydrodynamic model are based on the laws of conservation for mass, momentum, and energy. The model’s governing equations include the Navier-Stokes equations for fluid motion and the advection-diffusion equations for salinity (Hamrick, 1992, 1996; Hamrick and Wu, 1997) Horizontally, the equations are formulated in a curvilinear coordinate system. For vertical discretization, this model application uses sigma-stretched grids. Grid cells are discretized through a finite difference method using an explicit scheme. Water density is determined by temperature and salinity, following United Nations Educational, Scientific and Cultural Organization's equation of state (Millero et al., 1981).

Accompanying the EFDC+ model package is the Grid+V1.0 software (DSI, LLC, 2023), which was used to develop the curvilinear grid. The GRID+ software offers a GIS-based interface for building rectilinear, radial, and curvilinear grids. Grids developed in Grid+ can be directly imported into EFDC+. In Grid+, grids can be refined or coarsened in the x and y direction by a factor of any integer. The EFDC+ model has been used to simulate hydrodynamics and reactive transport across various environments, including rivers, lakes, reservoirs, wetlands, estuaries, and coastal areas. Many researchers have successfully used the model to simulate water level (Liu and Garcia, 2008), flow (Chen, Fang, and Devkota, 2016; Devkota and Fang, 2014; Liu and Garcia, 2008), and salinity (Alarcon et al., 2021; Devkota and Fang, 2014; Jeong et al., 2010; Liu et al., 2008; Xia et al., 2011). The EFDC+ has a user-friendly graphical user interface and mesh developer.

This study involves preparing five three-dimensional EFDC+ models of Biscayne Bay with five resolutions. Input data for the models, including bathymetry, water level, flow, salinity, water temperature, and atmospheric data, were obtained from Alarcon et al. (2022). According to Alarcon et al. (2022), the water-level data were obtained from the Virginia Key Station of the National Oceanic and Atmospheric Administration’s (NOAA) Tides and Currents Meteorological Observations website (NOAA, 2024). The water flow and salinity data were obtained from the South Florida Water Management District Environmental Monitoring website (SFWMD, 2024). Tidal water temperature data were obtained from NOAA’s Virginia Key Station (NOAA, 2024), and canal water temperature data were obtained from the South Florida Water Management District (SFWMD, 2024). Bathymetry is based on the one-third, arc-second mean lower low water bathymetric digital elevation model developed by NOAA's National Ocean Service (NCEI, 2018). More information about these data and the model boundary conditions is shown in Table 2. Figure 2 shows the locations of the boundary conditions and where the boundary condition data were measured.

Simulations were performed for a 2-year period, commencing on 1 January 2017 and concluding on 31 December 2018. The period from 1 January 2017 to 30 June 2017 was designated as the warm-up phase. The period from 1 July 2017 to 31 December 2018 was used to assess the models’ performance. All models used dynamic time stepping with an initial value of 0.05 seconds, a safety factor of 0.15, five growth steps, and a 30-second maximum time step. The growth step is the minimum number of iterations for each time step before increasing the time step for the dynamic stepping. The safety factor is used to determine the maximum stable time step. For dynamic time stepping, it should be a positive number greater than 0 and less than 1. The time step for model outputs was 1 hour.

The five models were run independently, and their simulations were compared with one another and with the observed data. Modeled water-surface elevation and salinity were compared with measured water-surface elevation and salinity at eight gauges: BISC70B, BISC60B, BISC44B, BISC36B, BISCD8, BISC12B, BISCA4, and BISC4B (Figure 2; SFWMD, 2024). Each of the eight measurement gauges are outfitted with conductivity, temperature, and pressure sensors that take a reading every 15 minutes.

Five grids of varying horizontal grid resolutions were developed (BB140; all grids were generated using Grid+V1.0). The study is based on an arbitrarily generated, medium-resolution model grid that comprises a, ∼160 m × 140 m grid resolution in north Biscayne Bay and an ∼273 m × 256 m resolution grid in central and South Biscayne Bay. This medium grid was developed for a previous Biscayne Bay model study (Alarcon, 2021). The model was assembled with a finer resolution in the north because of increased geomorphological complexity in that region (i.e. channels, islands, and outlets). The fine-resolution model was created by dividing the i direction and j direction of the medium grid by a factor of 2. The coarse1 grid was created by multiplying the i direction and j direction of the medium grid by a factor of 2; the coarse2 grid was developed by multiplying the i direction and j direction of the medium grid by a factor of 3; and the coarse3 grid was developed by multiplying the i direction and j direction of the medium grid by a factor of 4. Figure 3 shows the configurations of the model grid resolutions. The average cell size is 123 × 115 m for the fine grid, 245 × 230 m for the medium grid, 494 × 463 m for the coarse1 grid, 730 × 709 m for the coarse2 grid, and 974 × 949 m for the coarse3 grid. Table 3 shows the features of each of the grids.

Modeled water-surface elevation was compared with measured water-surface elevation at eight gauges: BISC70B, BISC60B, BISC44B, BISC36B, BISCD8, BISC12B, BISCA4, and BISC4B. Generally, the models followed similar trends, performed similarly to each other, and matched the measured data. During storm conditions, the models did a poorer job predicting water level at the southern gauges. The maximum difference between the average measured and average modeled water-surface elevation is 0.02 m.

Figure 4 shows the time series plots for modeled and measured data for 14 days from 2–16 September 2017, with Hurricane Irma hitting south Florida in the middle of this time period. Hurricane Irma was a Category 4 hurricane when it made landfall in Cudjoe Key, approximately 160 km SW of Biscayne Bay, on 10 September 2017. The modeled and measured water-surface elevation matched best during Hurricane Irma elevation matched poorest during Hurricane Irma at BISC4B, the southernmost gauge. The modeled water-surface elevation is markedly higher than measured water-surface elevation during the hurricane at both BISC4B and BISCA4, the two southernmost stations. Note that the measured water-surface elevation used to force all open, tidal boundary conditions is in the northern portion of the study domain, west of the Miami River (Figure 2). This is closest to station BISC70B and farthest from BISC4B. Additional measurements of water-surface elevation along the open, tidal boundary would likely improve the model results.

Table 4 presents the statistical assessment for water-surface elevation, including R², RMSE, and KGE. Similarly, Figure 5 shows a bar chart illustrating the statistical indicators across the different resolutions at different water-surface elevation stations. Table 4 and Figure 5 show that all resolutions at all stations were able to simulate water-surface elevation with an R² ranging between 0.34 and 0.86, a KGE ranging between 0.48 and 0.91, and RMSE ranging between 0.01 and 0.11 m. Results are best at the northernmost gauges and poorest at the southernmost gauges. This is likely because the measured water-surface elevation used to force all open, tidal boundary conditions is located in the northern portion of the study domain (Figure 2).

In general, model results of water-surface elevation improved with increasing grid resolution (Table 4, Figure 5), whereas the fine-resolution grid was an outlier, with slightly poorer results. The RMSE improved, on average, between the fine and coarse3 grids by −0.02 m (−17%); KGE improved, on average, by 0.03 m (10%); and R² improved, on average, by 0.09 m (16%). Both RMSE and KGE had similar results for the medium and coarse1 grid that were both better than the finest-scale grid, but the model performance decreased more for the coarse2 and coarse3 grids (Figure 5). The combined results from the three statistics, five grids, and eight calibration locations support the hypothesis that increasing grid resolution increases model performance of water-surface elevation; however, the finest-resolution model did not perform as well as the medium-resolution model.

Modeled salinity was compared with measured salinity at the same eight gauges as water-surface elevation: BISC70B, BISC60B, BISC44B, BISC36B, BISCD8, BISC12B, BISCA4, and BISC4B (Figure 6). As with water-surface elevation generally, the models followed similar trends, where each of the models performed similarly to each other and matched the measured data. The model is not able to simulate the variation in salinity that the measurements capture. This is evidenced by the fact that the measured standard deviation in salinity is greater than the modeled standard deviation in almost all cases (except D8 medium, coarse1, coarse2, coarse3 and 4B coarse2, coarse3). The maximum average difference between the average measured and average modeled salinity is 7 parts per thousand, which occurred at BISC 44B, where the model oversimulated measured salinity.

Table 5 displays the statistical assessment for salinity across the five grid resolutions at each of the eight gauges. Similarly, Figure 7 shows a bar chart of these statistical indicators. Table 5 and Figure 7 show that all resolutions at all stations were able to simulate salinity, with an R² ranging between 0.12 and 0.85, KGE ranging between 0.23 and 0.91, and RMSE ranging between 1.79 and 6.54 ppt.

Unlike the results for water-surface elevation, the salinity results do not consistently improve with increasing grid resolution. In fact, at most calibration points, results got worse with increasing grid resolution. Similarly to water-surface elevation, the fine-resolution grid was an outlier, with slightly poorer results for salinity. The RMSE changed, on average, between the fine and coarse3 grids by 0.45 (19%); KGE changed, on average, by −0.12 (21%); and R² changed, on average, by −0.09 ppt (19%). The combined results from the three statistics, five grids, and eight calibration locations do not support the hypothesis that increasing grid resolution improves model performance of salinity.

Most previous studies found that higher-grid resolutions lead to better model performance (Table 1). Conceptually, increasing grid resolution allows for a more realistic representation of bathymetry and the simulation of finer-scale spatial processes; therefore, it is logical to assume that increasing grid resolution should improve model performance. In the current study, this concept was supported for water-surface elevation but not supported for salinity. This finding does not infer that the model does a poor job in simulating either water-surface elevation or salinity. If grid resolution did not improve model results of salinity, other issues with the model may occur, preventing increasing resolution from increasing model accuracy. Fringer (2019) states that higher order–resolution grids do not imply better agreement with measurements because of boundary condition errors. Potential issues that may prevent higher-grid resolutions from leading to better model performance in this study may include limited observations for parameterizing boundary conditions, low vertical resolution, and simplified representation of bottom roughness.

Based on these findings, the recommended grid for achieving the highest model accuracy in simulations of water-surface elevation is the medium-resolution grid. The medium grid returns the best fit statistics and needs 27 hours to run. The coarse2 grid is another good option for simulating water-surface elevation because, although some accuracy is lost, it requires less than 1 hour to run. The percentage difference improves, on average, between the coarse2 and medium grids by 13% for RMSE, 7% for KGE, and 10% for R². It is difficult to make a recommendation for optimal grid resolution for salinity because no consistent trend that correlates salinity results and grid resolution occurs. Throughout the study site, different locations had better fits to observations at different grid resolutions, making it impossible to suggest that grid resolution provided better simulations. In any hydrodynamic modeling study, it is recommended that modelers develop and test more than one grid resolution to understand trade-offs between model accuracy and computation time before settling on a final grid resolution.

Modeled water-surface elevation did not capture the storm surge that occurred in the central and southern portions of Biscayne Bay during Hurricane Irma (Figure 4). In this study, boundary conditions used only one wind gauge to represent winds throughout the entire spatial model domain and one water-surface elevation gauge to represent tidal forcings along the eastern boundary condition. During a hurricane, in a region this size, the winds and storm surge may vary throughout the spatial domain. Future work simulating storms should use multiple wind gauges or a hindcast wind field and multiple water-surface elevation gauges to represent the open, tidal boundary.

Major limitations of this study are discussed here. There is only one location where water-surface elevation is measured in the study site, and it is at the open, tidal boundary. Similarly, there is only one location where salinity is measured at the open, tidal boundary. As a result, the boundary conditions along the eastern tidal boundary are not spatially varying. Improving the representation of spatially varying tidal boundary conditions may improve the model results.

This study assessed how adjusting grid resolution affects two modeled outputs: water-surface elevation and salinity. It did not test how grid resolution affects other model outputs such as flow, velocity, particle trajectories, or residence time.

In these simulations, each time the mesh resolution was refined or coarsened, the boundary conditions had to be redefined. For each resolution, open-boundary cells had to be reidentified. The selection of a cell as an open boundary can be subjective, especially in shallow areas. Additional studies could investigate how uncertainty in the selection of open-boundary cells affects model outputs.

This study is based on a hydrodynamic model of Biscayne Bay developed by Alarcon et al. (2022). Five new model grids with varying resolution—fine, medium, coarse1, coarse2, and coarse2—were developed. The average cell size for the grids is 130 × 130 m for the fine grid, 250 × 250 m for the medium grid, 500 x 500 m for the coarse1 grid, 800 × 800 m for the coarse2 grid, and 1000 × 1000 m for the coarse3 grid. The models were tested to understand how different grid resolutions affect the accuracy of water-surface elevation and salinity simulations. Modeled water-surface elevation and salinity were compared with measured data at eight stations. Measured and modeled results were compared using three statistical indicators of model fit: R², RMSE, and KGE.

The results of the study showed that the salinity and water-surface elevation results of the five models are closer to each other than they are to the measured data. None of the models were able to capture the storm surge that occurred during Hurricane Irma. The accuracy of simulated water-surface elevation improved with increasing grid resolution; however, the accuracy of simulated salinity did not improve with increasing grid resolution. Based on these results, the medium-resolution grid is recommended for simulations of water-surface elevation. Future model work should focus on acquiring measured data of salinity and water-surface elevation in additional locations near the open, tidal boundary to improve the spatial resolution of the boundary forcings.

This research was funded by a NOAA/Atlantic Oceanographic and Meteorological Laboratory grant to the Northern Gulf Institute (award number NA160AR4320199).