Biological and Environmental Research - Earth and Environmental System Sciences
Earth and Environmental System Modeling

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Demonstrate Advanced Capabilities for Representing Waves within Earth System Models, a Key Process in Coastal Storm Surge Impacts

Product Definition

Wind-generated waves are involved in several important processes in the global climate system. This includes the mediation of momentum, heat, and mass fluxes between the ocean and atmosphere (Cavaleri et al. 2012). Waves also play an important role in the cryosphere, where there are feedbacks between wave dissipation and sea ice fracture in the marginal ice zone (Squire et al. 1995). Of particular interest to U.S. Department of Energy (DOE) mission questions is the response of the water surface level to shoaling and breaking waves in coastal regions. This additional “wave setup” (Longuet-Higgins and Stewart 1964) can represent a large portion of the overall mean water surface elevation in tropical cyclone flooding events, with implications to energy infrastructure in coastal regions. The wave setup process is illustrated in Figure 1(a).

Wind waves occupy a portion of the energy/frequency spectrum that is distinct from the longer-period ocean waves (tides, storm surges, tsunamis, etc.), which are resolved in some ocean circulation models (Wright et al. 1999). Since wind waves have periods on the order of 1-10 seconds and wavelengths on the order of 10-100m, their time and length scales are too fine to be resolved explicitly over the entire globe. Therefore, “phase-averaged” wave models are typically employed in large-scale applications (Cavaleri et al. 2007). These models describe the evolution of wave action (which is closely related to wave energy) as it propagates in latitude, longitude, frequency, and directional space (Tolman 1991). The frequency/direction spectrum can then be used to calculate several statistical quantities describing the wave field such as significant wave height, mean direction, and mean period. Another important quantity is the Stokes drift, shown in Figure 1 (b), which is the mean velocity induced by wave motion in the propagation direction.

Since phase-averaged wave models resolve a frequency/direction spectrum at each model grid point in the ocean, the number of model unknowns is high. This large number of unknowns, combined with the complexity of wave physics parameterizations, which describe generation, dissipation, non-linear interactions, etc., makes these wave models very expensive additions to Earth system models.

Therefore, our goal is to use unstructured meshes in order to economically resolve wave processes globally across the open ocean and coastal regions of interest. Using these meshes, the computational expense associated with the high mesh resolution required for coastal regions can be balanced with efficient use of coarse resolution for open ocean basins. As will be shown in the results section, coarse unstructured meshes with coastal refinement can provide comparable accuracy to global high-resolution structured meshes. Unstructured meshes can achieve this level of accuracy at significantly reduced computational cost. This allows for an unprecedented capability to efficiently include wave processes at both global and coastal scales in Earth system models.

Product Documentation

The most recent version (6.07) of the National Oceanic and Atmospheric Administration (NOAA) WAVEWATCHIII® model has been integrated into the DOE Energy Exascale Earth System Model (E3SM) as the wave model component. Initially, the model used the traditional structured mesh configuration. However, in order to enable global-to-coastal wave modeling for E3SM, modifications were made to extend WAVEWATCHIII® to global, unstructured mesh domains. Previously, unstructured meshes had been used successfully in hurricane wave prediction studies but were limited to regional domains (Abdolali et al. 2020). Here, we implement and validate, for the first time, the performance of unstructured meshes for global domains with coastal refinements, which are appropriate for climate modeling applications within E3SM.

The triangular unstructured mesh considered in this study was generated using open-source mesh generation software (Roberts et al. 2019) and was designed to align with early versions of meshes under consideration for version two of E3SM (Hoch et al. 2020). The mesh has 2-degree resolution globally and transitions to ½-degree resolution in regions shallower than 4km. The 4km threshold was chosen to resolve coastal areas between the continental shelf break and the shoreline. A 10% element grade is enforced between the ½- and 2-degree resolution. The resolutions chosen allows the unstructured mesh to be readily compared against structured meshes with global uniform resolutions of ½ degree and 2 degrees. An image of the mesh is shown in Figure 2.

This global unstructured mesh capability has been validated against wave buoy measurements in order to assess overall suitability for use in E3SM, in terms of both accuracy and efficiency. We have compared modeled wave results for June-October 2005 with observations from the National Data Buoy Center (NDBC; Meindl and Hamilton 1992) along the U.S. coast. Additionally, the comparisons between the ½-degree and 2-degree structured meshes provide a sense of how well the unstructured mesh balances the accuracy and efficiency of the two different resolutions. The model was forced using atmospheric data from the Climate Forecast System Reanalysis (CFSR; Saha et al. 2010) product and was not coupled to other Earth system model components for this study.