Optimization, Finite Element Mesh, Tide and Storm Surge Modeling, Western North Atlantic Ocean


Recently, a highly resolved, finite element mesh was developed for the purpose of performing hydrodynamic calculations in the Western North Atlantic Tidal (WNAT) model domain. The WNAT model domain consists of the Gulf of Mexico, the Caribbean Sea, and the entire portion of the North Atlantic Ocean found west of the 60° W meridian. This high resolution mesh (333K) employs 332,582 computational nodes and 647,018 triangular elements to provide approximately 1.0 to 25 km node spacing. In the previous work, the 333K mesh was applied in a Localized Truncation Error Analysis (LTEA) to produce nodal density requirements for the WNAT model domain. The goal of the work herein is to use these LTEA-based element sizing guidelines in order to obtain a more optimal finite element mesh for the WNAT model domain, where optimal refers to minimizing nodes (to enhance computational efficiency) while maintaining model accuracy, through an automated procedure. Initially, three finite element meshes are constructed: 95K, 60K, and 53K. The 95K mesh consists of 95,062 computational nodes and 182,941 triangular elements providing about 0.5 to 120 km node spacing. The 60K mesh contains 60,487 computational nodes and 108,987 triangular elements. It has roughly 0.5 to 185 km node spacing. The 53K mesh includes 52,774 computational nodes and 98,365 triangular elements. This is a particularly coarse mesh, consisting of approximately 0.5 to 160 km node spacing. It is important to note that these three finite element meshes were produced automatically, with each employing the bathymetry and coastline (of various levels of resolution) of the 333K mesh, thereby enabling progress towards an optimal finite element mesh. Tidal simulations are then performed for the WNAT model domain by solving the shallow water equations in a time marching manner for the deviation from mean sea level and depth-integrated velocities at each computational node of the different finite element meshes. In order to verify the model output and compare the performance of the various finite element mesh applications, historical tidal constituent data from 150 tidal stations located within the WNAT model domain are collected and examined. These historical harmonic data are applied in two types of comparative analyses to evaluate the accuracy of the simulation results. First, qualitative comparisons are based on visual sense by utilizing plots of resynthesized model output and historical tidal constituents. Second, quantitative comparisons are performed via a statistical analysis of the errors between model response and historical data. The latter method elicits average phase errors and goodness of average amplitude fits in terms of numerical values, thus providing a quantifiable way to present model error. The error analysis establishes the 53K finite element mesh as optimal when compared to the 333K, 95K, and 60K meshes. However, its required time step of less than ten seconds constrains its application. Therefore, the 53K mesh is manually edited to uphold accurate simulation results and to produce a more computationally efficient mesh, by increasing its time step, so that it can be applied to forecast tide and storm surge in the Western North Atlantic Ocean on a real-time basis.


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Graduation Date





Hagen, Scott


Master of Science in Civil Engineering (M.S.C.E.)


College of Engineering and Computer Science


Civil and Environmental Engineering

Degree Program

Civil Engineering








Release Date

August 2005

Length of Campus-only Access


Access Status

Masters Thesis (Open Access)