A numerical simulation of summer circulation for Monterey Bay Le Ngoc Ly Department of Oceanography, Naval Postgraduate School

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1 A numerical simulation of summer circulation for Monterey Bay Le Ngoc Ly Department of Oceanography, Naval Postgraduate School Phu Luong Abstract A three dimensional coastal ocean system for Monterey Bay (MOB) is developed using numerical grid generation to study the summer circulation. The system is a primitive equation coastal ocean modeling system, which consists of a coastal ocean model, numerical grid generation routines, and a grid package which allows the model to be coupled to model grids. In this coastal ocean system, a curvilinear nearly-orthogonal (CNO) grid is used to enhance the model numerical solution. The MOB model has 28 sigma vertical levels, and the CNO coastlinefollowing numerical grid has 131 x 131 grid points, which cover a domain of 150 km by 150 km. The model has horizontal resolutions of 200 m to 2 km, free surface dynamics, and realistic coastlines and bottom bathymetry. The model code is written for a multi-block grid, but a single-block CNO grid is demonstrated for the MOB simulations. The MOB model and the associated grid are used to simulate summer circulation and reproduce the MOB basic physics such as coastal currents and upwelling locations. 1 Introduction Water circulation in the Monterey Bay (MOB) region is interesting and important for many human and scientific activities. MOB is called a "natural laboratory", because of many intensive investigation by physical, chemical, biological, meteorological and geological

2 270 Hydraulic Engineering Software oceanographers. The major problem that arises in circulation modeling in this region is that the MOB region is distinguished by the Monterey Submarine Canyon (MSC), which features some of the steepest topography encountered anywhere in the world ocean. The complicated bottom topography with seamounts and the MSC makes the MOB three dimensional water circulation difficult to simulate using a primitive equation ocean model with full turbulence closure. MOB is located 100 km south of San Francisco on the U.S. West Coast. There were a number of observational studies of the MOB region *. There were recent studies of the spring-summer (March-July) circulation in MOB by Rosenfeld et al. \ This time of year is characterized by strong upwelling and equatorward alongshore-component winds which result in the strongest near-surface temperature gradients and the largest biological productivity. During these periods, a band of cold water has been observed which flows equatorward across the mouth of Monterey Bay. These equatorward water flows have typical speeds of cm s~~* ^. Observations also show that upwelling centers are located north (near Ft. Ano Nuevo) and south (near Ft. Sur) of Monterey Bay. Studies by Rosenfeld et al. *'^ and Ramp et al. * also show that there is a warm anticyclonic feature which is often found off Monterey Bay. This feature was also seen from Advanced Very High Resolution Radiometer infrared imagery and Conductive Temperature Depth data in November, 1998 ^. Ly et al. ^'^ have shown that solutions of an ocean numerical model are strongly dependent on the grid used. A poorly suited grid may lead to unsatisfactory ocean model results *. An improper choice of grid point location can lead to instability or lack of convergence. The accurate representation of multi-scale physical phenomena in numerical models has long been a main concern of modelers. In ocean modeling, one of the main concerns of modelers is the simulation of the development, evolution, and interaction of various scales of physical phenomena from the small scale of turbulent dissipation to mesoscale eddies, fronts, and larger-scale flows. In this case, with limited computer resources, an appropriate choice of the numerical grid plays a key role in determining the quality of the numerical solution of a coastal ocean model ^. Traditionally, single-block rectangular (cartesian) grids have been most commonly used in coastal ocean modeling for their simplicity. However, the traditional grids (even with very high horizontal and vertical resolution) may not be well

3 Hydraulic Engineering Software 271 suited for the MOB region, which has extremely complicated bottom topography with the MOB submarine canyon, seamounts and very steep slopes at the continental shelf break. In our coastal ocean system, a curvilinear nearly-orthogonal (CNO), coastline-following grid is used to enhance model numerical solutions by better treating the MOB shelf break region and extremely complicated MOB bottom topography. Our CNO grid is crucial for the MOB ocean model because it can reduce by 40 % the MOB model horizontal pressure gradient errors in comparison with the traditional rectangular grid model ^. These grids are designed by using grid generation techniques **. This kind of grids can also easily increase horizontal resolution in the subregion of the model domain without increasing the computational expense with a higher resolution over the entire domain. This goal could be nearly achieved by a nesting technique (interactive nesting) with more complicated processes dealing with boundary conditions, but would be computationally much more expensive. The passive nesting lacks two-way interaction between coarse and fine resolution regions 12,13 Another problem related to nesting is the interaction between multiple nested meshes, particularly the tendency for propagating dispersive waves to discontinuously change their speeds upon passing from one mesh to the next and to reflect off the boundaries of each mesh ^'^. This problem is a big concern of the nesting technique. The purpose of this paper is to report on a numerical simulation of the Monterey Bay region circulation for the summer (July) period. 2 The MOB Ocean Circulation Model and Numerical Grid The model is a three dimensional primitive equation model which describes the velocity, surface elevation, salinity, and temperature fields in the ocean. The ocean is assumed to be hydrostatic and incompressible (Boussinesq approximation). The equations are written in a system of Cartesian coordinates with x eastward, y northward, and z upward. The motions induced by small-scale processes not directly resolved by the model grid (subgrid scale) are parameterized in terms of horizontal mixing processes. The horizontal diffusive terms are for parameterization of subgrid scale processes, but in practice

4 272 Hydraulic Engineering Software these horizontal diffusive terms are usually required to damp smallscale computational noise **. The modified Princeton Ocean Model 14 is used for the MOB summer circulation simulation. The model is a three dimensional primitive equation ocean circulation model with the second order turbulence closure to provide a parameterization of the vertical mixing process. The model has the curvilinear nearly-orthogonal multi-block grid coastal ocean system, but only the curvilinear single-block grid is used in the MOB study. The MOB coastal ocean circulation system consists of a coastal ocean model, numerical grid generation routines, and a grid package which allows the model to be coupled with model grids. The curvilinear orthogonal and nearly-orthogonal coastline-following single-block grid of the multi-block code is developed for MOB. The grid is shown in Fig. 1, which shows a high grid density packed along steep slopes and the Monterey Submarine Canyon. This grid reduces by 40 % the sigma coordinate errors in comparison with the traditional rectangular single-block gird. The MOB model has 131 X 131 horizontal grid points and covers a domain of approximately 150 km x 150 km. The horizontal resolution of the MOB model varies from 200 m to 2 km in the curvilinear grid. For clarity, the horizontal nearly-orthogonal grid in Fig. 1 is plotted with only every other grid line. The model has 28 vertical sigma levels, free surface dynamics, and realistic coastlines and bathymetry. Open lateral boundary conditions at the three open boundaries (north, south, west) for the barotropic current, temperature, and salinity are radiation conditions. The temperature and salinity are prescribed by July monthly mean observational values. The boundary conditions for surface elevation at the open boundaries are zero gradient normal to the open boundary. 3 The MOB Summer Circulation Simulation The coastal system for MOB is initialized with the July monthly mean values of climatological three dimensional temperature and salinity fields from all available datasets to date. The typical monthly mean wind for July is used for the system. The model is spun up for 30 days and run for 60 days. The simulations are computed on the CRAY-YMP supercomputers with four CPU (Naval Postgraduate School) and on the C90 with sixteen CPU (Stennis Space Center,

5 Hydraulic Engineering Software 273 MS) using multitasking modes. The external (barotropic) mode time step is 1 s, and the internal (baroclinic) mode time step is 40 s, so that the Courant-Friedrichs-Levy computational stability criterion is satisfied. The 90 day simulations are presented in Figs The summer (July) upwelling-favorable (equatorward alongshore component) winds in the Monterey Bay region, move surface water away from shore so that it must be replaced by colder and higher salinity upwelled water. This can be seen in Figs Fig. 2 shows surface currents at 90 days. From the contours, we can see the surface current field has energetic motions at coastal regions with more contours. This region has strong upwelling activity in the summer (upwelling centers) and strong coastal currents. The signatures of the upwelling and coastal current activity are shown by more contours in comparison with the rest of the model domain. The surface current vectors (which are not shown here) show more clearly the summer upwelling and coastal current activities. These equatorward currents have typical speeds of cm s~* (Fig. 2). This magnitude of the coastal cold equatorward current is also observed ^. The surface current vector field also shows an anticyclonic feature located at the southwestern region of the model domain. This warn anticyclonic feature was also observed *»*. The summer period of year is characterized by strong upwelling which is reproduced by our coastal ocean system for Monterey Bay. The upwelling location can be seen from the surface temperature contours of the 90-day model run, which are shown in Fig. 3. The upwelling region has a surface temperature of less than 11 C which is located near the northeastern part of the model domain (upwelling center) along the coastline across Monterey Bay. This upwelling location and surface temperature magnitude are observed *'*>*. Very similar features of upwelling can be seen from the model surface salinity field. The model surface salinity contours of the 90-day run are shown in Fig. 4. The upwelling region is located in the coastal region with a salinity greater than 33.4 psu in comparison with the surrounding region. The location and magnitude of the surface salinity field are observed ^. 4 Summary and Conclusions A three dimensional primitive equation coastal ocean system for Monterey Bay has been developed using numerical grid generation for

6 274 Hydraulic Engineering Software studying the summer circulation. The system consists of a coastal ocean model of Monterey Bay, numerical grid generation routines, and a grid package which allows the Monterey Bay model to be coupled with these grids. The model code is written for a multi-block grid, but only a single block CNO grid is used to enhance the model numerical solution. Our CNO grid places a high grid density along steep slopes and the Monterey Submarine Canyon. This grid reduces by 40 % the sigma coordinate errors in comparison with the traditional rectangular single-block gird. The model summer simulations with the associated grid for Monterey Bay show the basic physics of typical strong summer upwelling and equatorward cold and high salinity coastal currents. The upwelling locations, surface coastal current, and temperature and salinity magnitudes agree well with observed values. The model surface current of the 90-day run also shows a warm anticyclonic feature. Acknowledgments The support of the Office of Naval Research under grants N WR3I is gratefully acknowledged. References [1] Rosenfeld, L.K, Schwing, F.B, Garfield, N. & Tracy, D.L., Bifurcated flow from an upwelling center: a cold water source for Monterey Bay. Cont. Shelf Res., 14, 931, 1994a. [2] Rosenfeld, L.K., Schramm, R.E., Paduan, J.B, Hatcher, G.A. & Anderson, T., Hydrographic data collected in Monterey Bay during 1 September 1988 to 16 December, Technical Report, 94-15, Monterey Bay Aquarium Research Institute, 1994b. [3] Rosenfeld, L.K., Anderson, T., Hatcher, G., Roughgarden J. & Shkedy, Y., Upwelling fronts and barnacle recruitment in Central California, Technical Report95-19, Monterey Bay Aquarium Research Institute, 102 pp., [4] Ramp, S.R., Rosenfeld, L.K., Tisch, T.D. & Hicks, M.R., Moored observations of the current and temperature structure over the continental slope off central California. Part I: A basic description of the variability, J. Geophys. Res., 2, pp.20-25, 1996.

7 Hydraulic Engineering Software 275 [5] Tisch, T.D., Ramp, S.R. & Collins, C.A., Observations of the geostrophic current and water mass characteristics off Point Sur, California, from May 1988 through November J. Geophys. Res., 97, pp , [6] Ly, L.N. & Luong, P., Application of grid generation technique in coastal ocean modeling for the Mediterranean. American Geot/mon AGf/; TmnsacZwma, 74, 325, [7] Luong, P. & Ly, L.N., Application of multi-block grid technique in coastal ocean modeling: the Mediterranean simulation. AGU Transactions, O42B-9, No. 45, [8] Ly, L.N. & Jiang, L., Horizontal pressure gradient errors of the Monterey Bay sigma coordinate ocean model with various grids. J. Geophys. Res., (In press), [9] Ly, L.N. & Luong, P., Application of grid generation technique to the Yellow Sea simulation. High Performance Computing and Communication (UPC-ASIA 1995,), ElectronicProceedings, CD-ROM, Taipei, Taiwan, [10] Ly, L.N. & Luong, P,, A mathematical coastal ocean circulation system with breaking waves and numerical grid generation. Applied Mathematical Modelling, 10, 633, [11] Thompson, J.F., War si, Z.U. & Mastin, C.W., Numerical Grid Generation: Foundations and Applications (Elsevier Science Publishing Co., Inc.), p. 483, [12] Spall, M.A. & Holland, W.R., A nested primitive equation model for oceanic applications. J. Physic. Oceanogr., 21, 205, [13] Laugier, M., Angot, P. & Mortier, L., Nested grid methods for an ocean model: A comparative study. Int. J. Num. Methods in Fluids, 23, 1163, [14] Blumberg, A.F. & Mellor, G.L., A description of a threedimensional coastal ocean circulation model. Three- Dimensional Coastal Ocean Models, Coastal and Estuarine Sciences 4, pp AGU, Washington, D.C, 1987.

8 276 Hydraulic Engineering Software Longitude Fig. 1 Nearly-Orthogonal Curvilinear Grid u CD TD Longitude Fig. 2 Surface Current Contours

9 Hydraulic Engineering Software ) Santa Cruz -' Longitude Fig. 3 Surface Temperature Contours <D Santa Cruz Longitude Fig. 4 Surface Salinity Contours