Obf Oceanography 2006 19.Pdf

or collective redistirbution of any portion article of any by of this or collective redistirbution Th ADVANCES IN COMPUTATIONAL OCEANOGRAPHY articleis has been in published Oceanography , Volume 19, Number journal of Th 1, a quarterly , Volume BY OLIVER B. FRINGER, JAMES C. MCWILLIAMS, AND ROBERT L. STREET photocopy machine, reposting, or other means is permitted photocopy machine, only is reposting, means or other A New Hybrid Model 2006 by Th e Oceanography Society. Copyright FOR COASTAL SIMULATIONS with the approval of Th approval the with C. Blanco gran e Oceanographyis Society. All rights reserved. Permission or Th e [email protected] Society. Send to: all correspondence C. Mendocino Pt. Arena Pt. Reyes ted to copy this article for use in teaching and research. Repu article for use and research. this copy in teaching to ted e Oceanography Society, PO Box 1931, Rockville, MD 20849-1931, USA. blication, systemmatic reproduction, reproduction, systemmatic blication, 64 Oceanography Vol. 19, No. 1, Mar. 2006 PHYSICAL PROCESSES IN the world’s oceans span an which includes estuaries. Models that are specifi cally designed enormous range of spatio-temporal scales, from ocean circu- for coastal and estuarine processes include the Stanford Un- lation at the global scale down to dissipation and mixing at structured Nonhydrostatic Terrain-Following Adaptive Navier- the centimeter scale. It is impossible to simulate all of these Stokes Simulator (SUNTANS6), DELFT3D7, or the semi-implic- processes using one model due to the shear computing power it TRIM model of Casulli (1999). Coastal and estuarine pro- that would be required. Thus, different ocean models focus on cesses distinguish themselves most signifi cantly from regional specifi c processes and hence different spatio-temporal scales. At and global processes in that they result from the interaction of the largest scales are the global ocean circulation models, such ocean currents with complex boundaries and steep bathym- as the Parallel Ocean Program (POP1), which is used primar- etry. Models that simulate even smaller-scale processes, such ily to simulate seasonal or climactic processes (i.e., the El Niño as wind-waves, do not compute the three-dimensional circula- Southern Oscillation [ENSO] or thermohaline circulation). tion, but instead focus on computing time-averaged effects that At the intermediate scales are the regional ocean models, such can be included in larger-scale coastal circulation models, such as the Princeton Ocean Model (POM2), the Regional Ocean as Simulating WAves Nearshore (SWAN8), a two-dimensional Modeling System (ROMS3,4), or the MIT General Circulation wind-wave model. Model (MITgcm5), which are well suited to modeling regional A hybrid model is generated when two or more models that processes such as the Gulf Stream or the California Coastal focus on distinct spatio-temporal scales are coupled to form a Current. Indeed, these models are not necessarily limited to simulation tool that can capture a larger range of spatio-tempo- regional circulation studies; they have been applied extensively ral scales. With the advent of high-performance computing, the to simulate global circulation and, at the smaller scale, coastal hybrid concept has gained popularity in recent years, combining processes, such as upwelling and internal waves. Ocean models the expertise behind different model development programs. In that are specifi cally designed to simulate this end of the spatio- this article, a new hybrid simulation tool that is under develop- temporal spectrum are referred to as “coastal ocean models,” ment is presented. It attempts to tackle the problem of simulat- which, like their regional modeling counterparts, are not nec- ing regional circulation using ROMS while correctly incorporat- essarily limited to, but are best suited for, the coastal region, ing the effects of smaller-scale coastal processes with SUNTANS. 1 http://climate.lanl.gov/Models/POP; 2 http://www.aos.princeton.edu/WWWPUBLIC/htdocs.pom; 3 http://www.atmos.ucla.edu/cesr/ROMS_page.html; 4 http://marine.rutgers.edu/po/index.php?model=roms; 5 http://mitgcm.org; 6 http://suntans.stanford.edu; 7 http://www.wldelft.nl/soft/d3d/intro; 8 http://www.wldelft.nl/soft/swan Oceanography Vol. 19, No. 1, Mar. 2006 65 THE IMPORTANCE OF THE GRID motion would be computed. This type of per off soon. Assuming that it does not, All ocean models represent discrete so- simulation would require a total of 1022 however, and assuming that the simula- lutions of an approximate form of the grid cells, which would in turn require tion started today and was continuously Navier-Stokes equations. These equa- time-step sizes of 0.1 sec if we would ex- transferred to improved computer sys- tions govern the motion of fl uid within pect to resolve the temporal behavior of tems as they emerged, the estimate of 333 the oceans at all scales, ranging from motions at such small scales. A year-long million years surprisingly reduces down global circulation scales down to mix- simulation of the ocean, then, would to a much more manageable 40 years. ing and dissipative scales for processes require 315 million time steps. Because A computation time of 40 years might like double-diffusion and turbulence in average simulation codes require roughly suggest that a direct numerical simula- breaking internal waves. In some regions 100 mathematical operations per grid tion of the oceans is not too far off in of the ocean, these processes can be as cell per time step, a DNS of the ocean the distant future. However, even if a small as a few centimeters. Because fl uid would require a total of 3 x 1030 opera- system were devised that made such a motions do not vary much at such small tions. If we had access to the world’s fast- tremendous simulation feasible, it would scales (they are smeared out by viscos- est supercomputer, Blue Gene, which is be impossible to provide initial condi- ity), we could represent, in principle, located at Lawrence Livermore National tions such as salinity, temperature, and the full range of scales of motion in the Laboratory and is capable of perform- velocity and wave-height fi elds with such oceans if we were to discretize them with ing roughly 300 trillion operations per high resolution. In addition, it would not cells that were one cubic centimeter in second, then our simulation would take be possible to provide high-resolution volume. A discrete solution of the fl ow 333 million years! This, of course, is at boundary conditions such as bathymetry fi eld represented by these fi nite volumes the present rate of computing power, (we would need to know every detail using the Navier-Stokes equations would which, according to Moore’s law, is dou- about every sand ripple and every coral be a so-called direct numerical simula- bling roughly every 18 months. Although reef!) or heat-fl ux and wind-stress fi elds. tion (DNS) of all of the world’s oceans, Moore’s prediction has stood the test of Furthermore, the shear volume of data and it would eliminate the need for a time over the past two decades, it is likely that would result would be unmanage- turbulence model because all scales of that computing power may begin to ta- able. The alternative, of course, is what ab Figure 1. Diff erent grid arrangements designed to capture multi-scale physics in the vicinity of a boundary (red line). (a) Grid stretching to resolve a straight boundary. (b) Grid stretching with a curvilinear grid near a relatively smooth boundary. (c) A curvilinear grid near sharply varying topography, which requires masking (gray cells) since the topography varies too quickly. (d) Th e masking procedure can also be per- formed with Cartesian grids, but the boundary is not followed as closely as in (c). (e) An unstructured grid allows for high resolution near irregular topography without the use of masking. 66 Oceanography Vol. 19, No. 1, Mar. 2006 members of the ocean and atmosphere enable the analysis of a broad range of est (Figure 1a). Of course, because most modeling communities have been doing scales by employing complex gridding boundary layers occur near complex for over half a century. Instead of com- techniques and advanced methods of dis- topography, a bulk of ocean models, in puting all the scales of motion, simpli- cretizing the governing continuous equa- fact all of those mentioned in the intro- fi cations of the Navier-Stokes equations tions most accurately, such as high-order duction except for SUNTANS and TRIM, are devised such that their discrete solu- advection schemes or high-order time- employ curvilinear grids that can fol- tions are more tractable. The basic prem- stepping techniques. Given an advanced low topographic features while employ- ise behind all numerical simulations is discretization technique, the premise be- ing grid stretching to resolve boundary that because computing power dictates hind the accurate simulation of problems layers in the vicinity of coastal features the number of points that will be used to involving a broad range of length scales is (Figure 1b). This practice of employing discretize a given problem of interest, it that most multi-scale fl ows of interest are sets the range of scales that will be simu- well represented by larger-scale motions, Oliver B. Fringer ([email protected]) lated by a discretization of the equations while a smaller percentage of the fl ows is Assistant Professor, Department of Civil themselves, while the effects of the re- contain small-scale physics that require and Environmental Engineering, Stanford maining set of motions (often referred to computationally expensive high resolu- University, Stanford, CA, USA. James C. as subgrid-scale motions) are parameter- tion. The simplest example of a multi- McWilliams is Louis B.

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