A High-Resolution Coupled Riverine Flow, Tide, Wind, Wind Wave, and Storm Surge Model for Southern Louisiana and Mississippi, Part I: Model Development and Validation

MWR2010aA coupled system of wind, wind wave, and coastal circulation models has been implemented for southern Louisiana and Mississippi to simulate riverine flows, tides, wind waves, and hurricane storm surge in the region. The system combines the NOAA Hurricane Research Division Wind Analysis System (H*WIND) and the Interactive Objective Kinematic Analysis (IOKA) kinematic wind analyses, the Wave Model (WAM) offshore and Steady-State Irregular Wave (STWAVE) nearshore wind wave models, and the Advanced Circulation (ADCIRC) basin to channel-scale unstructured grid circulation model. The system emphasizes a high-resolution (down to 50m) representation of the geometry, bathymetry, and topography; nonlinear coupling of all processes including wind wave radiation stress-induced set up; and objective specification of frictional parameters based on land-cover databases and commonly used parameters. Riverine flows and tides are validated for no storm conditions, while winds, wind waves, hydrographs, and high water marks are validated for Hurricanes Katrina and Rita.

S Bunya, JC Dietrich, JJ Westerink, BA Ebersole, JM Smith, JH Atkinson, RE Jensen, DT Resio, RA Luettich Jr, CN Dawson, VJ Cardone, AT Cox, MD Powell, HJ Westerink, HJ Roberts (2010). “A High-Resolution Coupled Riverine Flow, Tide, Wind, Wind Wave, and Storm Surge Model for Southern Louisiana and Mississippi, Part I: Model Development and Validation.Monthly Weather Review, 138, 345-377.

Development of Storm Surge Which Led to Flooding in St. Bernard Polder during Hurricane Katrina

OE2010Hurricane Katrina caused devastating flooding in St. Bernard Parish, Louisiana. Storm surge surrounded the polder that comprises heavily populated sections of the Parish in addition to the Lower 9th Ward section of Orleans Parish. Surge propagated along several pathways to reach levees and walls around the polder’s periphery. Extreme water levels led to breaches in the levee/wall system which, along with wave overtopping and steady overflow, led to considerable flood water entering the polder. Generation and evolution of the storm surge as it propagated into the region is examined using results from the SL15 regional application of the ADCIRC storm surge model. Fluxes of water into the region through navigation channels are compared to fluxes which entered through Lake Borgne and over inundated wetlands surrounding the lake. Fluxes through Lake Borgne and adjacent wetlands were found to be the predominant source of water reaching the region. Various sources of flood water along the polder periphery are examined. Flood water primarily entered through the east and west sides of the polder. Different peak surges and hydrograph shapes were experienced along the polder boundaries, and reasons for the spatial variability in surge conditions are discussed.

BA Ebersole, JJ Westerink, S Bunya, JC Dietrich, MA Cialone (2010). “Development of Storm Surge Which Led to Flooding in St. Bernard Polder during Hurricane Katrina.Ocean Engineering, 37, 91-103.

Mass Residuals as a Criterion for Mesh Refinement in Continuous Galerkin Shallow Water Models

JHY2008Mass balance error has been computed traditionally by using conventional fluxes derived from the conservation of mass equation, but recent literature supports a method based on fluxes that are consistent with the discretization of the governing equations. By comparing the mass residuals from these two methods to the truncation errors produced by the discretization of the governing equations, we show that the conventional fluxes produce mass residuals that are more descriptive of the overall behavior of the model, i.e., they are better correlated with truncation error. Then we demonstrate that these mass residuals can be used as a criterion for mesh refinement. In an example using a one-dimensional shallow water model, we demonstrate that, by moving nodes from regions with large mass residuals to regions with small mass residuals, a mesh can be developed that shows less truncation error than a mesh developed by using localized truncation error analysis. And, in an example using a two-dimensional shallow water model, we demonstrate that the computed solution can be improved in regions with large mass residuals through mesh refinement.

JC Dietrich, RL Kolar, KM Dresback (2008). “Mass Residuals as a Criterion for Mesh Refinement in Continuous Galerkin Shallow Water Models.ASCE Journal of Hydraulic Engineering, 134(5), 520-532.

On the Form of the Momentum Equation for Shallow Water Models Based on the Generalized Wave Continuity Equation: Conservative vs. Non-Conservative

AWR2005Nearly all generalized wave continuity (GWC)-based models utilize the velocity-based, non-conservative form of the momentum equation to obtain the depth-averaged changes in velocity. It has been hypothesized that a flux-based, conservative form of the momentum equation may improve accuracy and stability. Herein, we study the impact of the choice of dependent variable and form of the momentum equation in a GWC-based finite element shallow water model. The impact of this change on mass balance, stability, and accuracy (spatial and temporal) is rigorously assessed, first for 1D barotropic flows and then for 2D barotropic flows in a variety of basins. Both 1D and 2D results indicate that the conservative form improves mass balance on both global and local scales, with the most significant gains found in local mass balance in areas with steep bathymetry gradients. This is also the region where the conservative form shows an increase in local spatial accuracy. Taylor series analysis and numerical simulations indicate a strong correlation between local spatial truncation errors and local mass balance errors. Stability, temporal accuracy and global spatial accuracy do not show statistically significant changes between the two algorithms in both 1D and 2D studies.

KM Dresback, RL Kolar, JC Dietrich (2005). “On the Form of the Momentum Equation for Shallow Water Models Based on the Generalized Wave Continuity Equation: Conservative vs. Non-Conservative.Advances in Water Resources, 28(4), 345-358.

A 2D Implicit Time-Marching Algorithm for Shallow Water Models Based on the Generalized Wave Continuity Equation

IJNMF2004This paper builds upon earlier work that developed and evaluated a 1D predictor-corrector time-marching algorithm for wave equation models and extends it to 2D. Typically, the generalized wave continuity equation (GWCE) utilizes a three time-level semi-implicit scheme centred at k, and the momentum equation uses a two time-level scheme centred at k + 1/2. It has been shown that in highly non-linear applications, the algorithm becomes unstable at even moderate Courant numbers. This work implements and analyses an implicit treatment of the non-linear terms through the use of an iterative time-marching algorithm in the two-dimensional framework. Stability results show at least an eight-fold increase in the maximum time step, depending on the domain. Studies also examined the sensitivity of the G parameter (a numerical weighting parameter in the GWCE) with results showing the greatest increase in stability occurs when 1 <= G/Tmax <= 10, a range that coincides with the recommended range to minimize errors. Convergence studies indicate an increase in temporal accuracy from first order to second order, while overall error is less than the original algorithm, even at higher time steps. Finally, a parallel implementation of the new algorithm shows that it scales well.

KM Dresback, RL Kolar, JC Dietrich (2004). “A 2D Implicit Time-Marching Algorithm for Shallow Water Models Based on the Generalized Wave Continuity Equation.International Journal for Numerical Methods in Fluids, 45(3), 253-274.