By Jose E. Castillo
Our oceans are the last physical frontier on Earth, covering 70% of the planetary surface and changing constantly. Yet ocean dynamics are poorly understood and extremely complex. Changes in the ocean affect not only the ocean ecosystem, but also weather and food production, among other things. By studying and modeling coastal ocean dynamics, one can draw important conclusions about the entire global ocean and ultimately forecast the health of our planet. Eventually, these models will benefit understanding of the impact of changes in the ocean, so that together we can find ways to protect our only remaining collective human resource. Such research will also indirectly provide important information allowing the government to forecast changes affecting defense strategies, navigation applications, and the mainland.
Numerical models are essential for creating estimates of oceanographic and environmental variables, the latter being useful when making water system predictions in coastal areas. Another important aspect of numerical models is their innate responsiveness and subsequent increase in resolution, which can be applied to real locations, such as the San Diego Bay and Monterey Bay, located on the California coast. These two areas are defined as local regions and require approximately <100 m of resolution to accurately study phenomena such as internal waves, internal bores, biogeochemical processes, red tides, and oil spills. However, model errors are inevitable, due to uncertainties resulting from utilization of mathematical approximations. While modern observational hardware systems operating at these time and space scales are becoming more and more accurate, the required resolutions result in models that are extremely computationally expensive. But due to advances in computational model methods and computer hardware capabilities, it is possible to develop models that are capable of running these types of simulations.
The need for more precise coastal ocean models that can improve the performance of existing global and regional models motivates such research. In addition, it is desirable that models take better advantage of specialized and commercially-available, high-performance computing (HPC) resources and services (referred to as a computational environment, or CE) typically used by these high-end applications. The "Oceanography in 2025" workshop, organized by the National Academy of Sciences in 2009, addressed the need for such modeling. Workshop participants reached several conclusions: that the oceanographic community should make these models accessible to non-expert applied users; that users should be able to take "off the shelf" model components, assemble the right combination of dynamical core, parameterization, and data assimilation infrastructure for a particular application, and complete this process in a "reasonable amount of time;" and that the final application should guarantee accurate results. Moving towards a generalized 3D curvilinear geometry will help to increase the model resolution.
Models with coarse resolutions don’t always maintain important information about underwater terrain. For instance, models with spatial resolution as low as 5–25 km smooth the underwater topography—or bathymetry—and omit most of the undulations on the terrain; this results in low slopes throughout and the removal of most of the structure on the terrain. Therefore, the bathymetry effect on flow is either ignored or damped. The interaction of eddies with realistic bathymetry is crucial in the simulation of dominant ocean features that result from its interactions with major coastal bathymetry abutments. Moving towards the finer resolution models preserves more structures on the terrain but increases the slope. Hence, the distribution of the grid points in the vertical direction becomes more important in order to control the grid-induced numerical errors.
Figure 1. Architecture of the General Curvilinear Environmental Model computational environment (GCEM-CE). The diagram shows the main components and their roles.
The General Curvilinear Coastal Ocean Model (GCCOM) is capable of resolving these high resolution nonlinear processes [1]. The GCCOM model solves the 3D Navier Stokes equations within the Boussinesq approximation and is capable of simulating nonhydrostatic flow. One of the most important features of this model is its use of general curvilinear coordinates in the three dimensions. GCCOM was built to resolve high-resolution problems (tenths of a meter). It provides a more accurate way of solving for the pressure gradient and is able to deal with very steep topographies. GCEM provides support for weak couplings between pairs of computational models through the Distributed Coupling Toolkit (DCT) [4]. It also incorporates a data assimilation framework, which can improve the model accuracy and efficiency for real-time forecasting [5]. Another feature of the model is the multiscale interaction with the Regional Ocean Model System (ROMS), which allows external forcing interchange in sub-mesoscale processes for nearshore systems [3]. Some of the current issues in high resolution coastal ocean modeling are results of the demanding computational cost associated with the amount of data generated. We have developed a parallel version of the model based on Fortran 90/95 and the Message Passing Interface (MPI) to reduce simulation run times [6]. A further goal of the GCEM group is to provide a Cyber-infrastructure Web Application Framework (CyberWeb), through which scientists can run customized simulations and the general public can run test simulations, view results, and download data through a community portal [7].
Fully 3D Curvilinear Coordinates enable the model to easily adapt to the 3D real physical space of the study region. This differs from the sigma coordinate traditionally used by coastal models, which is designed to adapt to only the horizontal bathymetry, cannot represent non-convexity in the vertical, and clearly affects the calculation of different oceanic variables, particularly on steep slopes. Furthermore, the majority of commonly-used ocean models use hydrostatic assumption to calculate pressure. In the coastal regions and on fast-varying slopes, this assumption will lead to considerable error in the pressure calculation, which affects the entire system of the ocean. Moreover, there is a need for detailed studies of the different subjects on high-resolution ocean models, including biogeochemical studies, where the hydrostatic assumption will fail.
A new hybrid model, ROMS-GCCOM, nests the high-resolution and non-hydrostatic GCCOM within the regional scale hydrostatic Regional Ocean Modeling System (ROMS). This hybrid model is a tool for efficient exploration of the interaction of processes that occur on a wide range of temporal and spatial scales. For example, ROMS-GCCOM will allow the exploration of the relative influence of large-scale conditions, such as upwelling/downwelling cycles, thermocline depth, ambient stratification, and mesoscale currents, on the shoaling of internal waves and the resulting nearshore internal bore field [3]. Some regions already in preparation for study with the hybrid model include the San Diego Bay (Figure 2, left), where the model will use data collected through the Southern California Coastal Ocean Observing System (SCCOOS), and the Monterey Bay (Figure 2, right), where high-resolution observational data of shoaling internal waves are available. The San Diego Bay project is in collaboration with Dr. Yi Chao at University of California, Los Angeles, and the Monterey Bay study is in collaboration with Drs. Ryan Walter and Paul Choboter at California Polytechnic State University.
Figure 2. San Diego Bay (left) and Monterey Bay (right) 3D curvilinear Mesh [2, 8].
Collaboration with the National Center for Atmospheric Research (NCAR) helped develop the Data Assimilation Research Testbed (DART) interface to the GCCOM. The DART-GCCOM assimilation system is enabled for multivariate assimilation of several ocean data sets. This includes satellite surface temperature and altimetry data, in-situ temperature, and salinity and velocity data, including high-frequency radar surface current measurements. Data assimilation has the ability to improve the speed and quality of coastal ocean model development and is becoming an integral part of that process. With the GCCOM, this research group demonstrates how data assimilation can be used with a non-hydrostatic coastal ocean model to study sub-mesoscale processes and accurately estimate the state variables.
The coastal ocean dynamics group has been developing a computational environment (CE) that includes a parallel, MPI framework. The CyberWeb system includes a wide range of capabilities from user account and group management, data management, dynamic discovery and use of configured services and resources, as well as visualization services.
This article is based, in part, on a minisymposium on coastal ocean dynamics presented at the 2015 SIAM Conference on Mathematical and Computational Issues in the Geosciences (GS15).
Acknowledgments: This work was supported in part by the National Science Foundation (Grants #0753283, #0721656), the Department of Energy (DOE # DE-GC02-02ER25516), the CSU Council on Ocean Affairs, Science and Technology (COAST), and with resources available with an NSF funded XSEDE allocation, and the San Diego State University Computational Sciences Research Center.
References
[1] Abouali, M., & Castillo, J. E. (2013). Unified Curvilinear Ocean Atmosphere Model (UCOAM): A vertical velocity case study. Math. Comput. Model., 57(9-10), 2158–2168.
[2] Bucciarelli, R., Garcia, M., & Castillo, J. E. (2015). General Curvilinear Ocean Model Application: Complete Three-Dimensional Modeling of San Diego Bay Hydrodynamics. Applied Computational Science and Engineering Student Support (ACSESS). San Diego State University.
[3] Choboter, P., Thomas, M., & Castillo, J. E. (2015). Nesting Nonhydrostatic UCOAM within Hydrostatic ROMS In Soc. Ind. Appl. Math. Math & Comp. Issues in Geosciences.
[4] De Cecchis, D., Drummond, L.A., & Castillo, J. E. (2013). Design of a Distributed Coupling Toolkit for High Performance Computing Environment. Math. Comput. Model., 57(9-10), 2267-2278.
[5] Garcia, M., Hoar, T., Thomas, M., Bailey, B., and Castillo, J. E. (submitted 2015). GCCOM-DART: Ensemble Data Assimilation Analysis System for Sub-mesoscale Processes, Sensitivity Analysis for a 3D Nonhydrostatic Model.
[6] Thomas, M. (2014). Parallel Implementation of the Unified Curvilinear Ocean and Atmospheric (UCOAM) Model and Supporting Computational Environment. Thesis (PhD). The Claremont Graduate University, AAT 3617676; ISBN: 9781303853449; Volume: 75-08(E), Section: B. p. 110.
[7] Thomas, M., & Castillo, J. E. (2009).Development of a Computational Environment for the General Curvilinear Ocean Model. J. Phys.: Conf. Ser.,180(1), 012030.
[8] Torres, C. R., Mueller, J., Trees, C., & Castillo, J. E. (2007). Tridimensional Circulation in Curvilinear Coordinates: Application to Monterey Bay. American Geophysical Union (AGU), Spring Meeting.
Jose E. Castillo is the director of the Computational Science Research Center (CSRC), founder and director of the joint doctoral program in computational science, and Claremont Graduate University (CGU) Professor in the Department of Mathematics and Statistics at San Diego State University.