# Structured (SHOC)

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SHOC (Sparse Hydrodynamic Ocean Code) is the hydrodynamic model used by the CEM. This model has evolved over the last 10 years from MECO (Model of Estuaries and Oceans) and prior to that M3D. SHOC is a general purpose model (Herzfeld, 2006) based on the paper of Blumberg and Herring (1987), applicable on spatial scales ranging from estuaries to regional ocean domains. It is a three-dimensional finite-difference hydrodynamic model, based on the primitive equations. Outputs from the model include three-dimensional distributions of velocity, temperature, salinity, density, passive tracers, mixing coefficients and sea-level. Inputs required by the model include forcing due to wind, atmospheric pressure gradients, surface heat and water fluxes and open-boundary conditions (e.g. tides). The model is based on the equations of momentum, continuity and conservation of heat and salt, employing the hydrostatic and Boussinesq assumptions. The equations are discretized on a finite-difference stencil corresponding to the Arakawa C grid.

The model uses a curvilinear orthogonal grid in the horizontal and a choice of fixed ‘z’ coordinates or terrain following sigma coordinates in the vertical. The ‘z’ vertical system allows for wetting and drying of surface cells, useful for maintaining fine vertical resolution near the surface in the presence of large sea level fluctuations, or modelling regions such as tidal flats where large areas are periodically dry. The bottom topography is represented using partial cells (Pacanowski and Gnandadesikan, 1998). The model has a free surface and uses mode-splitting (Simons, 1974) to separate the two-dimensional (2D) mode from the three-dimensional (3D) mode. Mode-splitting allows fast moving gravity waves to be solved independently from the slower moving internal waves, allowing the 2D and 3D modes to operate on different time-steps, for computational efficiency. The model uses explicit time-stepping throughout, except for the vertical diffusion scheme which is implicit. A Laplacian diffusion scheme is employed in the horizontal on geopotential surfaces. Smagorinsky mixing coefficients may be utilized in the horizontal (Griffies and Hallberg, 2000).

The ocean model can invoke several turbulence closure schemes, including k-e, k-w, Mellor-Yamada 2.0, 2.5 and Csanady-type parameterisations. A variety of advection schemes may be used on tracers, and 1st or 2nd order can be used for momentum. The model also contains a suite of radiation, extrapolation, sponge and direct data forcing open-boundary conditions. SHOC is capable of utilizing multi-processors in a shared memory environment, which increases run-times almost linearly with processors used. The model uses a sparse coordinate system internally (Herzfeld, 2006) that efficiently represents wet cells only, and allows arbitrary domain decomposition for multi-processing to ensure load balance. In its general use, the model is capable of performing particle tracking and may be directly coupled to ecological and sediment transport models. SHOC may be configured to operate in 2-D depth averaged mode, or a 2-D vertical slice may be simulated. Extensive diagnostics exist, including momentum and 2D vorticity balances. Point source / sinks may be included at arbitrary locations for inputting fluxes of volume, tracer or momentum. SHOC supports automated model setup, where the model parameters are estimated from grid and bathymetric information, requiring minimal user input. Also included in SHOC is a transport mode, where velocities saved offline may be used to advect and diffuse tracers; e.g. sediment transport and biogeochemisty may operate using the transport mode. The transport mode may use a semi-Lagrangian advection scheme which is unconditionally stable, allowing the time-step to be increased to result in run-times orders of magnitude faster. Using the sparse format to save inputs to the transport model can decrease storage requirements by over 80%. The transport model may also be used as a simple data converter, where data read in may be saved in a different format. The model is supported by a detailed User Guide (Herzfeld and Waring, 2008) and Science Manual (Herzfeld et al., 2008).

**Blumberg, A.F., Herring, J. (1987)** Circulation modelling using orthogonal curvilinear coordinates, in Three-Dimensional Models of marine and Estuarine Dynamics, Ed. J.C.J. Nihoul and B.M. Jamart, Elsevier.

**Griffes, S.M., Hallberg, R. W. (2000)** Biharmonic friction with a Smagorinsky viscosity for use in large-scale eddy-permitting ocean models. Mon. Weath. Rev., 128, 2935-2946.

**Herzfeld, M. (2006)** An alternative coordinate system for solving finite difference ocean models. Ocean Modelling, 14, 174 – 196.

**Herzfeld, M., Waring J. R. (2008)** SHOC: Sparse Hydrodynamic Ocean Code User’s manual. CSIRO internal document. 128 pp.

**Herzfeld, M., Waring, J., Parslow, J., Margvelashvili, N., Sakov, P., Andrewartha, J. (2008)** SHOC: Sparse Hydrodynamic Ocean Code Science manual. CSIRO internal document. 121 pp.

**Pacanowski, R.C. and Gnanadesikan, A. (1998)** Transient response in a z-level ocean model that resolves topography with partial-cells. Monthly Weather Review, 126, 3248–3270.

**Simons, T.J. (1974)** Verification of numerical models of lake Ontario. Part I, circulation in spring and early summer. J. Phys. Oceanog., 4, 507 – 523.