Predicting and Modeling Sea Level Rise in the Barnegat Bay
Abstract
Barnegat Bay is a key lagoonal back-barrier estuarine system that plays a large role in the economic activity and ecosystem of the New Jersey coast. As the largest body of water in New Jersey, over half a million people affect it annually through nutrient pollution and runoff. In order to further understand the anthropogenic impact, many studies have been conducted to model the bay. Despite these models giving researchers an idea of the different properties of a bay system, they do not take advantage of computational advancements that have occurred in recent years or account for changing parameters, such as sea level rise. The SCHISM open-source program has several libraries in order to model the hydrodynamics of water, taking into account wind, the Coriolis effect, baroclinic differences, and depth. Utilizing this model and bathymetric data, a current model of Barnegat Bay was formulated. The study suggests that poor circulation in the northern part of the bay is a result of the decreased outflow from urbanization, providing evidence that increased eutrophication in the northern bay could be a result from the poor circulation in that area. The mathematics utilized to analyze these relationships can be applied to other key bodies of water.
Data and Visualization
In order to create the model, 32,678 elevation data points across the Barnegat Bay were collected by the United States Geological Survey. The data can be seen here as a raster plot, contour plot, and bathymetry plot.
Generating the 3-Dimensional Mesh
In order to evaluate the simulation, the area and shape of Barnegat Bay had to be defined. However, mathematically there is no easy way to define such irregular shapes without being computationally intensive. Therefore, a Delaunay triangulation algorithm was implemented in order to define the area using a tessellation of triangles. There are several methods to applying a Delaunay triangulation, but the most computationally efficient is the divide and conquer approach. It runs in a O(Nlog N) time, and therefore works best for this study (Lee & Schacter, 1980). Using SMS by Aquaveo, a GIS map projection of Barnegat Bay was placed onto the interface. Then, a series of feature arcs were generated, encompassing the part of the bay that had data present. An arc represents a conceptual model of a feature in the system. In this case, the arc represents the shoreline for the entire bay. Once the feature arcs were produced encompassing the bay, a Spline fit algorithm was performed in order to smooth out the perimeter of the feature arc connections. This adds more realism to the model and removes the sharp edges that were originally present (Lange, 1986).
Once a smooth curve was generated around Barnegat Bay in SMS, the Delaunay triangulation had to be performed. For three points A, B, and C, they are connected by a circle circumscribing a triangle inside. The algorithm must determine if point D is inside the circle. After determining the determinant, if the value is greater than 0, then it can be concluded that the point lies within the circle (Figure 3). The matrixes for points A, B, C, and D is defined by the following:
The divide and conquer method for finding Delaunay triangles uses random distributions to choose vertices and generates the two possible triangles that can be made from them (Lee & Schacter, 1980). It then checks which one is a Delaunay triangle and which one is not, and chooses the former to be utilized.
This was implemented into SMS, which generated the triangulated mesh of Barnegat Bay. However, in order to add the depth and 3-dimensionality to the mesh, it had to be interpolated to the elevation data gathered. The data was imported and contained an x, y, and z coordinate for each elevation value. The mesh was then interpolated, where each data value in the triangles were averaged in order to be assigned to the node where the triangles intersected. A visual representation of the mesh and interpolation was generated.
Conducting Simulation
A SRH-2D simulation was implemented in SMS. This model first treats water as an incompressible fluid and derives the Navier-Stokes equation. Deriving this equation can yield the 1-dimensional St. Venant equation, which describes the flow of a fluid below a pressure surface. Then, these 2D depth-averaged dynamic wave equations can be solved using a finite-volume numerical method, which is a method of solving partial differential equations. Basically, each node on the mesh is assigned a volume, and then each term for the differential equation at this point is converted to an integral, which is then evaluated as a flux. This method is advantageous for this model, as it works easily for unstructured meshes that may have some errors in its geometry (Hwang, 2013). The model treated the simulation as a steady state flow, where diffusion occurs at a constant rate over time. An unsteady state flow is more realistic; however, it comes at the cost of computational strain. As a result, to simplify the model and allow for easier implementation, a steady state flow simulation was conducted (Deissler, 1965). Additionally, a wetting/drying algorithm was implemented in order to account for any errors made by the previous equations. This is because typically, older hydrodynamic models have treated the coast as a stable boundary that is unchanging. However, this is untrue, as the coast periodically changes from wet to dry and back to wet as tides/waves change (Medeiros & Hagen, 2012). Finally, the model control parameters were set. The start time was set to 0 hours, time-step set to 5 seconds, and the end time was set to how long the simulation should run. The simulation outputs a contour plot and vector field of the circulation of water in the system, where the length of the vector corresponds to the velocity of water flow at that point. The simulation outputs velocity magnitude, direction, basin stress, water depth, water elevation & pressure, and finally the Froude number. This is a dimensionless number that defines the ratio flow inertia to the external field. If this value is less than 1, it means the water at the point is undergoing subcritical flow, where the flow velocity is less than the wave velocity. If the value is greater than 1, it is undergoing supercritical flow (Vaughan, & O’Malley, 2005). These parameters were then simulated and modeled over the time steps to produce a vector field of the circulation patterns.
Discussion
The Barnegat Bay is undergoing a variety of struggles, including eutrophication from intensive nutrient loading and the looming threat of sea level rise. With these problems getting worse, it is crucial to mathematically model and extrapolate different functions of the bay, as it is impossible to observe everything firsthand. However, the lack of mathematical models for Barnegat Bay in comparison to other well-known bays is stunning. Therefore, this study sought out to design a hydrodynamic model using several mathematical principles and the open-source SMS modeling system by Aquaveo. The model clearly portrayed the poor circulation patterns in the northern part of the bay, and helped visualize how the northern and southern parts of the bay differ topographically. As urbanization has increased over the last few decades, including bridges, canals, and dredges, it has decreased the efficiency in which the bay flushes itself. This is especially apparent by the northern end of the bay by the Point Pleasant Inlet, which was found to have decreased circulation (Kennish, et al., 2015). The shallow water has less velocity and is not able to leave the system as quickly, and it recirculates any harmful pathogens/nutrients much more quickly than if the water was deep (Zalesny, & Ivchenko, 2015). A case study was also applied to the model. In order to observe the possible effects of sea level rise in the coming decades, several simulations were run with different water surface elevations at the inlets. According to the vector fields produced for both bed shear stress and Froude numbers, the model suggests that sea level rise will have an adverse effect on the southern portion of the bay, specifically the area near Oyster Creek power plant in Forked River. With just a 2 feet increase in water surface elevation, water velocity increased drastically towards the mainland. This will be detrimental to coastal communities, as flooding will be exacerbated in the Forked River coastline, along with increased erosion. Bed shear stress also increased significantly in this area, meaning that the water will be able to carry larger sediment sizes. Furthermore, Froude number was observed to increase in that area along with the Point Pleasant area as well. A high Froude number means the water flows more rapidly in the system. As a result, the model suggests that sea level rise will further have a negative impact on the more pristine southern portion of the bay in the coming decades through severe flooding, erosion, and disturbance of the ecosystem.
Full Poster
References
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