A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers
TL;DR: A preconditioner is used which, in the hydrostatic limit, is an exact integral of the Poisson operator and so leads to a single algorithm that seamlessly moves from nonhydrostatic to hydrostatic limits, competitive with the fastest ocean climate models in use today.
Abstract: The numerical implementation of an ocean model based on the incompressible Navier Stokes equations which is designed for studies of the ocean circulation on horizontal scales less than the depth of the ocean right up to global scale is described. A "pressure correction" method is used which is solved as a Poisson equation for the pressure field with Neumann boundary conditions in a geometry as complicated as that of the ocean basins. A major objective of the study is to make this inversion, and hence nonhydrostatic ocean modeling, efficient on parallel computers. The pressure field is separated into surface, hydrostatic, and nonhydrostatic components. First, as in hydrostatic models, a two-dimensional problem is inverted for the surface pressure which is then made use of in the three-dimensional inversion for the nonhydrostatic pressure. Preconditioned conjugate-gradient iteration is used to invert symmetric elliptic operators in both two and three dimensions. Physically motivated preconditioners are designed which are efficient at reducing computation and minimizing communication between processors. Our method exploits the fact that as the horizontal scale of the motion becomes very much larger than the vertical scale, the motion becomes more and more hydrostatic and the three- dimensional Poisson operator becomes increasingly anisotropic and dominated by the vertical axis. Accordingly, a preconditioner is used which, in the hydrostatic limit, is an exact integral of the Poisson operator and so leads to a single algorithm that seamlessly moves from nonhydrostatic to hydrostatic limits. Thus in the hydrostatic limit the model is "fast," competitive with the fastest ocean climate models in use today based on the hydrostatic primitive equations. But as the resolution is increased, the model dynamics asymptote smoothly to the Navier Stokes equations and so can be used to address small- scale processes. A "finite-volume" approach is employed to discretize the model in space in which property fluxes are defined normal to faces that delineate the volumes. The method makes possible a novel treatment of the boundary in which cells abutting the bottom or coast may take on irregular shapes and be "shaved" to fit the boundary. The algorithm can conveniently exploit massively parallel computers and suggests a domain decomposition which allocates vertical columns of ocean to each processing unit. The resulting model, which can handle arbitrarily complex geometry, is efficient and scalable and has been mapped on to massively parallel multiprocessors such as the Connection Machine (CM5) using data-parallel FORTRAN and the Massachusetts Institute of Technology data-flow machine MONSOON using the implicitly parallel language Id. Details of the numerical implementation of a model which has been designed for the study of dynamical processes in the ocean from the convective, through the geostrophic eddy, up to global scale are set out. The "kernel" algorithm solves the incompressible Navier Stokes equations on the sphere, in a geometry as complicated as that of the ocean basins with ir- regular coastlines and islands. (Here we use the term "Navier Stokes" to signify that the full nonhydrostatic equations are being employed; it does not imply a particular constitutive relation. The relevant equations for modeling the full complex- ity of the ocean include, as here, active tracers such as tem- perature and salt.) It builds on ideas developed in the compu- tational fluid community. The numerical challenge is to ensure that the evolving velocity field remains nondivergent. Most
Citations
More filters
TL;DR: An unstructured grid, finite-volume, three-dimensional (3D) primitive equation ocean model has been developed for the study of coastal oceanic and estuarine circulation as discussed by the authors.
Abstract: An unstructured grid, finite-volume, three-dimensional (3D) primitive equation ocean model has been developed for the study of coastal oceanic and estuarine circulation. The model consists of momentum, continuity, temperature, salinity, and density equations and is closed physically and mathematically using the Mellor and Yamada level-2.5 turbulent closure submodel. The irregular bottom slope is represented using a s-coordinate transformation, and the horizontal grids comprise unstructured triangular cells. The finite-volume method (FVM) used in this model combines the advantages of a finite-element method (FEM) for geometric flexibility and a finite-difference method (FDM) for simple discrete computation. Currents, temperature, and salinity in the model are computed in the integral form of the equations, which provides a better representation of the conservative laws for mass, momentum, and heat in the coastal region with complex geometry. The model was applied to the Bohai Sea, a semienclosed coastal ocean, and the Satilla River, a Georgia estuary characterized by numerous tidal creeks and inlets. Compared with the results obtained from the finite-difference model (ECOM-si), the new model produces a better simulation of tidal elevations and residual currents, especially around islands and tidal creeks. Given the same initial distribution of temperature in the Bohai Sea, the FVCOM and ECOM-si models show similar distributions of temperature and stratified tidal rectified flow in the interior region away from the coast and islands, but FVCOM appears to provide a better simulation of temperature and currents around the islands, barriers, and inlets with complex topography.
1,436 citations
TL;DR: In this paper, the Navier Stokes model on the sphere has been used to model the global circulation of the ocean, from the convective scale to the global scale, and a solution strategy has been proposed to deal with small-scale phenomena which are not in hydrostatic balance.
Abstract: Ocean models based on consistent hydrostatic, quasi-hydrostatic, and nonhydrostatic equation sets are formulated and discussed. The quasi-hydrostatic and nonhydrostatic sets are more accurate than the widely used hydrostatic primitive equations. Quasi-hydrostatic models relax the precise balance between gravity and pressure gradient forces by including in a consistent manner cosine-of-latitude Coriolis terms which are neglected in primitive equation models. Nonhydrostatic models employ the full incompressible Navier Stokes equations; they are required in the study of small-scale phenomena in the ocean which are not in hydrostatic balance. We outline a solution strategy for the Navier Stokes model on the sphere that performs efficiently across the whole range of scales in the ocean, from the convective scale to the global scale, and so leads to a model of great versatility. In the hydrostatic limit the Navier Stokes model involves no more computational effort than those models which assume strict hydrostatic balance on all scales. The strategy is illustrated in simulations of laboratory experiments in rotating convection on scales of a few centimeters, simulations of convective and baroclinic instability of the mixed layer on the 1- to 10-km scale, and simulations of the global circulation of the ocean.
1,302 citations
Filippo Giorgi1, Erika Coppola1, Fabien Solmon1, Laura Mariotti1, Mouhamadou Bamba Sylla1, X. Bi1, N. Elguindi1, G. T. Diro1, Vijayakumar S. Nair1, Graziano Giuliani1, Ufuk Utku Turuncoglu1, Stefano Cozzini, Ivan Güttler, Travis A. O'Brien2, Ahmed B. Tawfik3, A. Shalaby4, A. S. Zakey5, Allison L. Steiner, Frode Stordal6, Lisa C. Sloan2, Čedo Branković •
TL;DR: A new version of the RegCM regional climate modeling system, RegCM4, has been recently developed and made available for public use as discussed by the authors, which includes new land surface, planetary boundary layer, and air-sea flux schemes, a mixed convection and tropical band configuration, modifications to the pre-existing radiative transfer and boundary layer schemes, and a full upgrade of the model code towards improved flexibility, portability, and user friendliness.
Abstract: A new version of the RegCM regional climate modeling system, RegCM4, has been recently developed and made available for public use. Compared to previous versions, RegCM4 includes new land surface, planetary boundary layer, and air–sea flux schemes, a mixed convection and tropical band configuration, modifications to the pre-existing radiative transfer and boundary layer schemes, and a full upgrade of the model code towards improved flexibility, portability, and user friendliness. The model can be interactively coupled to a 1D lake model, a simplified aerosol scheme (including organic carbon, black carbon, SO4, dust, and sea spray), and a gas phase chemistry module (CBM-Z). After a general description of the model, a series of test experiments are presented over 4 domains prescribed under the CORDEX framework (Africa, South America, East Asia, and Europe) to provide illustrative examples of the model behavior and sensitivities under different climatic regimes. These experiments indicate that, overall, RegCM4 shows an improved performance in several respects compared to previous versions, although further testing by the user community is needed to fully explore its sensitivities and range of applications.
1,106 citations
TL;DR: In this article, the authors review what is known about the convective process in the open ocean, in which the properties of large volumes of water are changed by intermittent, deep-reaching convection, triggered by winter storms.
Abstract: We review what is known about the convective process in the open ocean, in which the properties of large volumes of water are changed by intermittent, deep-reaching convection, triggered by winter storms. Observational, laboratory, and modeling studies reveal a fascinating and complex interplay of convective and geostrophic scales, the large-scale circulation of the ocean, and the prevailing meteorology. Two aspects make ocean convection interesting from a theoretical point of view. First, the timescales of the convective process in the ocean are sufficiently long that it may be modified by the Earth's rotation; second, the convective process is localized in space so that vertical buoyancy transfer by upright convection can give way to slantwise transfer by baroclinic instability. Moreover, the convective and geostrophic scales are not very disparate from one another. Detailed observations of the process in the Labrador, Greenland, and Mediterranean Seas are described, which were made possible by new observing technology. When interpreted in terms of underlying dynamics and theory and the context provided by laboratory and numerical experiments of rotating convection, great progress in our description and understanding of the processes at work is being made.
1,098 citations
Cites methods from "A finite-volume, incompressible Nav..."
...The model [Marshall et al., 1997b] was configured with realistic geometry and topography with sufficient horizontal resolution (0.18) to capture the baroclinic instability of the mixed patch, as is evident in Figure 36b....
[...]
TL;DR: In this article, the authors estimate a time series of geocenter anomalies from a combination of data from the GravityRecoveryandClimateExperiment (GRACE)satellitemission and the output from ocean models.
Abstract: [1] In this study, we estimate a time series of geocenter anomalies from a combination of data from the GravityRecoveryandClimateExperiment(GRACE)satellitemissionandthe outputfromoceanmodels.Amatrixequationisderivedrelating totalgeocentervariations to the GRACE coefficients of degrees two and higher and to the oceanic component of the degree one coefficients. We estimate the oceanic component from two state-of-the-art ocean models. Results are compared to independent estimates of geocenter derived from other satellite data, such as satellite laser ranging and GPS. Finally, we compute degree one coefficients that are consistent with the processing applied to the GRACE Level-2 gravity field coefficients. The estimated degree one coefficients can be used to improve estimates of mass variability from GRACE, which alone cannot provide them directly.
664 citations
Additional excerpts
...The first is a version of the MIT general circulation model [Marshall et al., 1997] that is run at Jet Propulsion Laboratory (JPL) as part of the Estimating the Circulation and Climate of the Ocean (ECCO) consortium....
[...]
References
More filters
[...]
17,845 citations
TL;DR: In this paper, a new technique is described for the numerical investigation of the time-dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free The full Navier-Stokes equations are written in finite-difference form, and the solution is accomplished by finite-time step advancement.
Abstract: A new technique is described for the numerical investigation of the time‐dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free The full Navier‐Stokes equations are written in finite‐difference form, and the solution is accomplished by finite‐time‐step advancement The primary dependent variables are the pressure and the velocity components Also used is a set of marker particles which move with the fluid The technique is called the marker and cell method Some examples of the application of this method are presented All non‐linear effects are completely included, and the transient aspects can be computed for as much elapsed time as desired
5,841 citations
01 Jan 1977
TL;DR: The 12-layer UCLA general circulation model encompassing troposphere and stratosphere (and superjacent 'sponge layer') is described and selection of space finite-difference schemes for homogeneous incompressible flow, with/without a free surface, nonlinear two-dimensional nondivergent flow, enstrophy conserving schemes, momentum advection schemes, vertical and horizontal difference schemes, and time differencing schemes are discussed.
Abstract: The 12-layer UCLA general circulation model encompassing troposphere and stratosphere (and superjacent 'sponge layer') is described. Prognostic variables are: surface pressure, horizontal velocity, temperature, water vapor and ozone in each layer, planetary boundary layer (PBL) depth, temperature, moisture and momentum discontinuities at PBL top, ground temperature and water storage, and mass of snow on ground. Selection of space finite-difference schemes for homogeneous incompressible flow, with/without a free surface, nonlinear two-dimensional nondivergent flow, enstrophy conserving schemes, momentum advection schemes, vertical and horizontal difference schemes, and time differencing schemes are discussed.
1,741 citations
TL;DR: In this paper, the Navier Stokes model on the sphere has been used to model the global circulation of the ocean, from the convective scale to the global scale, and a solution strategy has been proposed to deal with small-scale phenomena which are not in hydrostatic balance.
Abstract: Ocean models based on consistent hydrostatic, quasi-hydrostatic, and nonhydrostatic equation sets are formulated and discussed. The quasi-hydrostatic and nonhydrostatic sets are more accurate than the widely used hydrostatic primitive equations. Quasi-hydrostatic models relax the precise balance between gravity and pressure gradient forces by including in a consistent manner cosine-of-latitude Coriolis terms which are neglected in primitive equation models. Nonhydrostatic models employ the full incompressible Navier Stokes equations; they are required in the study of small-scale phenomena in the ocean which are not in hydrostatic balance. We outline a solution strategy for the Navier Stokes model on the sphere that performs efficiently across the whole range of scales in the ocean, from the convective scale to the global scale, and so leads to a model of great versatility. In the hydrostatic limit the Navier Stokes model involves no more computational effort than those models which assume strict hydrostatic balance on all scales. The strategy is illustrated in simulations of laboratory experiments in rotating convection on scales of a few centimeters, simulations of convective and baroclinic instability of the mixed layer on the 1- to 10-km scale, and simulations of the global circulation of the ocean.
1,302 citations
Related Papers (5)
Eugenia Kalnay, Masao Kanamitsu, Robert Kistler, William D. Collins, D.G. Deaven, L. S. Gandin, M. Iredell, Suranjana Saha, Glenn H. White, John S. Woollen, Yuejian Zhu, Muthuvel Chelliah, Wesley Ebisuzaki, Wayne Higgins, John E. Janowiak, Kingtse C. Mo, Chester F. Ropelewski, Julian X. L. Wang, Ants Leetmaa, Richard W. Reynolds, Roy L. Jenne, Dennis Joseph