A Discontinuous Galerkin Coupled Wave Propagation/Circulation Model

JSC2014On large geographic scales, ocean waves are represented in a spectral sense via the action balance equation, which propagates action density through both geographic and spectral space. In this paper, a new computational spectral wave model is developed by using discontinuous Galerkin (DG) methods in both geographic and spectral space. DG methods allow for the use of unstructured geographic meshes and higher-order approximations for action propagation in both geographic and spectral space, which we show leads to increased accuracy. This DG spectral wave propagation model is verified and validated through comparisons to manufactured and analytic solutions as well as to the Simulating WAves Nearshore (SWAN) model. Coupled wave/circulation models are needed for many applications including for the interaction between waves and currents during daily wind and tide driven flows. We loosely couple the newDGspectralwavemodel to the DG Shallow Water Equation Model (DG-SWEM), an existing DG circulation model. In addition to formulating the DG method for the coupled wave/circulation model, we derive an a priori error estimate. Preliminary numerical results of the DG coupled wave/circulation model are presented with comparisons to DG-SWEM coupled tightly to SWAN.

JD Meixner, JC Dietrich, CN Dawson, M Zijlema, LH Holthuijsen (2014). “A Discontinuous Galerkin Coupled Wave Propagation/Circulation Model.Journal of Scientific Computing, 59, 334–370, DOI: 10.1007/s10915-013-9761-5.

U.S. IOOS Coastal and Ocean Modeling Testbed: Evaluation of Tide, Wave, and Hurricane Surge Response Sensitivities to Mesh Resolution and Friction in the Gulf of Mexico

JGR2013bThis paper investigates model response sensitivities to mesh resolution, topographical details, bottom friction formulations, the interaction of wind waves and circulation, and nonlinear advection on tidal and hurricane surge and wave processes at the basin, shelf, wetland, and coastal channel scales within the Gulf of Mexico. Tides in the Gulf of Mexico are modestly energetic processes, whereas hurricane surge and waves are highly energetic. The unstructured-mesh, coupled wind-wave and circulation modeling system, SWAN+ADCIRC, is implemented to generate modeled tidal harmonic constituents and hurricane waves and surge for a Hurricane Ike (2008) hindcast. In the open ocean, mesh resolution requirements are less stringent in achieving accurate tidal signals or matching hurricane surge and wave responses; however, coarser resolution or the absence of intertidal zones decreases accuracy along protected nearshore and inland coastal areas due to improper conveyance and/or lateral attenuation. Bottom friction formulations are shown to have little impact on tidal signal accuracy, but hurricane surge is much more sensitive, especially in shelf waters, where development of a strong shore-parallel current is essential to the development of Ike’s geostrophic setup. The spatial and temporal contributions of wave radiation stress gradients and nonlinear advection were charted for Ike. Nonlinear advection improves model performance by capturing an additional 10–20 cm of geostrophic setup and increasing resonant cross-shelf waves by 30–40 cm. Wave radiation stress gradients improve performance at coastal stations by adding an extra 20–40 cm to water levels.

PC Kerr, RC Martyr, AS Donahue, ME Hope, JJ Westerink, RA Luettich Jr, AB Kennedy, JC Dietrich, CN Dawson, HJ Westerink (2013). “U.S. IOOS Coastal and Ocean Modeling Testbed: Evaluation of Tide, Wave, and Hurricane Surge Response Sensitivities to Mesh Resolution and Friction in the Gulf of Mexico.Journal of Geophysical Research: Oceans, 118, 4633-4661, DOI: 10.1002/jgrc.20305.

Hindcast and Validation of Hurricane Ike (2008) Waves, Forerunner, and Storm Surge

JGR2013aHurricane Ike (2008) made landfall near Galveston, Texas, as a moderate intensity storm. Its large wind field in conjunction with the Louisiana-Texas coastline’s broad shelf and large scale concave geometry generated waves and surge that impacted over 1000 km of coastline. Ike’s complex and varied wave and surge response physics included: the capture of surge by the protruding Mississippi River Delta; the strong influence of wave radiation stress gradients on the Delta adjacent to the shelf break; the development of strong wind driven shore-parallel currents and the associated geostrophic setup; the forced early rise of water in coastal bays and lakes facilitating inland surge penetration; the propagation of a free wave along the southern Texas shelf; shore-normal peak wind-driven surge; and resonant and reflected long waves across a wide continental shelf. Preexisting and rapidly deployed instrumentation provided the most comprehensive hurricane response data of any previous hurricane. More than 94 wave parameter time histories, 523 water level time histories, and 206 high water marks were collected throughout the Gulf in deep water, along the nearshore, and up to 65 km inland. Ike’s highly varied physics were simulated using SWAN+ADCIRC, a tightly coupled wave and circulation model, on SL18TX33, a new unstructured mesh of the Gulf of Mexico, Caribbean Sea, and western Atlantic Ocean with high resolution of the Gulf’s coastal floodplain from Alabama to the Texas-Mexico border. A comprehensive validation was made of the model’s ability to capture the varied physics in the system.

ME Hope, JJ Westerink, AB Kennedy, PC Kerr, JC Dietrich, CN Dawson, CJ Bender, JM Smith, RE Jensen, M Zijlema, LH Holthuijsen, RA Luettich Jr, MD Powell, VJ Cardone, AT Cox, H Pourtaheri, HJ Roberts, JH Atkinson, S Tanaka, HJ Westerink, LG Westerink (2013). “Hindcast and Validation of Hurricane Ike (2008) Waves, Forerunner,
and Storm Surge.
Journal of Geophysical Research: Oceans, 118, 4424-4460, DOI: 10.1002/jgrc.20314.

Real-Time Forecasting and Visualization of Hurricane Waves and Storm Surge Using SWAN+ADCIRC and FigureGen

IMA2013Storm surge due to hurricanes and tropical storms can result in significant loss of life, property damage, and long-term damage to coastal ecosystems and landscapes. Computer modeling of storm surge is useful for two primary purposes: forecasting of storm impacts for response planning, particularly the evacuation of vulnerable coastal populations; and hindcasting of storms for determining risk, development of mitigation strategies, coastal restoration, and sustainability. Model results must be communicated quickly and effectively, to provide context about the magnitudes and locations of the maximum waves and surges in time for meaningful actions to be taken in the impact region before a storm strikes.

In this paper, we present an overview of the SWAN+ADCIRC modeling system for coastal waves and circulation. We also describe FigureGen, a graphics program adapted to visualize hurricane waves and storm surge as computed by these models. The system was applied recently to forecast Hurricane Isaac (2012) as it made landfall in southern Louisiana. Model results are shown to be an accurate warning of the impacts of waves and circulation along the northern Gulf coastline, especially when communicated to emergency managers as geo-referenced images.

JC Dietrich, CN Dawson, JM Proft, MT Howard, G Wells, JG Fleming, RA Luettich Jr, JJ Westerink, Z Cobell, M Vitse, H Lander, BO Blanton, CM Szpilka, JH Atkinson (2013). “Real-Time Forecasting and Visualization of Hurricane Waves and Storm Surge Using SWAN+ADCIRC and FigureGen.Computational Challenges in the Geosciences, The IMA Volumes in Mathematics and its Applications, 156, 49-70, DOI: 10.1007/978-1-4614-7434-0_3.

Limiters for Spectral Propagation Velocities in SWAN

OM2013As phase-averaged spectral wave models continue to grow in sophistication, they are applied more frequently throughout the ocean, from the generation of waves in deep water to their dissipation in the nearshore. Mesh spacings are varied within the computational domain, either through the use of nested, structured meshes or a single, unstructured mesh. This approach is economical, but it can cause accuracy errors in regions where the input parameters are under-resolved. For instance, in regions with a coarse representation of bathymetry, refraction can focus excessive wave energy at a single mesh vertex, causing the computed solution to become non-physical. Limiters based on the Courant–Friedrichs–Lewy (CFL) criteria are proposed for the spectral propagation (refraction and frequency shifting) velocities in SWAN. These limiters are not required for model stability, but they improve accuracy by reducing local errors that would otherwise spread throughout the computational domain. As demonstrated on test cases in deep and shallow water, these limiters prevent the excessive directional turning and frequency shifting of wave energy and control the largest errors in under-resolved regions.

JC Dietrich, M Zijlema, P-E Allier, LH Holthuijsen, N Booij, JD Meixner, JK Proft, CN Dawson, CJ Bender, A Naimaster, JM Smith, JJ Westerink (2012). “Limiters for Spectral Propagation Velocities in SWAN.Ocean Modelling, 70, 85-102, DOI: 10.1016/j.ocemod.2012.11.005.

The Surge Standard for "Events of Katrina Magnitude"

PNAS2013Hurricane Katrina was historic in magnitude. From ref. 1: “The large size of Katrina throughout its history, combined with the extreme waves generated during its most intense phase, enabled this storm to produce the largest storm surges (reliable observations up to 28 ft) that have ever been observed within the Gulf of Mexico, as determined from analyses of historical records.” The analysis by Grinsted et al. of the effects of rising temperatures on the frequency of Atlantic hurricane surge invokes “events of Katrina magnitude” as a standard by which other events are judged. However, we believe the Katrina benchmark, as used, is seriously flawed, in large part because the tide gauge spatial resolution used was so coarse that none of the locations forming the index ever experienced a true surge event of Katrina magnitude. This casts doubt on the claim that Katrina-level surge events may occur many times per decade by the late 21st century.

AB Kennedy, JC Dietrich, JJ Westerink (2013). “The Surge Standard for ‘Events of Katrina Magnitude.’Proceedings of the National Academy of Sciences of the United States of America, 110(29), E2665-E2666, DOI: 10.1073/pnas.1305960110.