ROMS model description\
The basic model system used is ROMS: The Regional Ocean Model System (http://www.myroms.org/)
is a freesurface, hydrostatic, primitive equation ocean model that uses stretched,
terrainfollowing coordinates in the vertical and orthogonal curvilinear coordinates in the horizontal.
The Regional Ocean Modeling System (ROMS) framework diagram illustrates various computational pathways:
standalone or coupled to atmospheric and/or wave models. It follows the Earth System Modeling Framework (ESMF) conventions
for model coupling: initialize, run and finalize. The dynamical kernel of ROMS is comprised of four separate models
including the nonlinear (NLM), tangent linear (TLM), representer tangent linear (RPM),
and adjoint (ADM). There are several drivers to run each model (NLM, TLM, RPM, and ADM) separately and together.
The drivers shown in the propagator group are used for Generalized Stability Theory (GST) analysis (Moore et al., 2004)
to study the dynamics, sensitivity, and stability of ocean circulations to naturally occurring perturbations,
errors or uncertainties in forecasting system, and adaptive sampling. The driver for adjoint sensitivities (ADSEN)
computes the response of a chosen function of the model circulation to variations
in all physical attributes of the system (Moore et al., 2006). It includes drivers for strong (S4DVAR, IS4DVAR)
and weak (W4DVAR) constraint variational data assimilation (Arango et al., 2006; Di Lorenzo et al., 2006).
A driver for ensemble prediction is available to perturb forcing and/or initial conditions along the most
unstable directions of the state space using singular vectors.
Finally, several drivers are included in the sanity check group to test the accuracy
and correctness of TLM, RPM, and ADM algorithms.
ROMS is a freesurface, terrainfollowing, primitive equations ocean model widely used
by the scientific community for a diverse range of applications
(e.g., Haidvogel et al., 2000; Marchesiello et al., 2003; Peliz et al., 2003; Di Lorenzo, 2003;
Dinniman et al., 2003; Budgell, 2005; Warner et al., 2005a, b; Wilkin et al., 2005).
The algorithms that comprise ROMS computational nonlinear kernel are described in detail in Shchepetkin and McWilliams (2005),
and the tangent linear and adjoint kernels and platforms are described in Moore et al. (2004).
ROMS includes accurate and efficient physical and numerical algorithms and several coupled models for biogeochemical,
biooptical, sediment, and sea ice applications. It also includes several vertical mixing schemes (Warner et al., 2005a),
multiple levels of nesting and composed grids.
For computational economy, the hydrostatic primitive equations for momentum are solved using a splitexplicit timestepping scheme
which requires special treatment and coupling between barotropic (fast) and baroclinic (slow) modes.
A finite number of barotropic time steps, within each baroclinic step, are carried out to evolve
the freesurface and vertically integrated momentum equations.
In order to avoid the errors associated with the aliasing of frequencies resolved by the barotropic steps
but unresolved by the baroclinic step, the barotropic fields are time averaged before they replace those values
obtained with a longer baroclinic step. A cosineshape time filter, centered at the new time level,
is used for the averaging of the barotropic fields (Shchepetkin and McWilliams, 2005).
In addition, the separated timestepping is constrained to maintain exactly both volume
conservation and consistancy preservation properties which are needed for the tracer equations
(Shchepetkin and McWilliams, 2005). Currently, all 2D and 3D equations are timediscretized
using a thirdorder accurate predictor (LeapFrog) and corrector (AdamsMolton)
timestepping algorithm which is very robust and stable.
The enhanced stability of the scheme allows larger time steps, by a factor of about four,
which more than offsets the increased cost of the predictorcorrector algorithm.
In the vertical, the primitive equations are discretized over variable topography using stretched terrainfollowing coordinates
(Song and Haidvogel, 1994). The stretched coordinates allow increased resolution in areas of interest,
such as thermocline and bottom boundary layers. The default stencil uses centered,
secondorder finite differences on a staggered vertical grid.
Options for higher order stencil are available via a conservative, parabolic spline reconstruction
of vertical derivatives (Shchepetkin and McWilliams, 2005). This class of model exhibits stronger sensitivity to topography
which results in pressure gradient errors. These errors arise due to splitting of the pressure gradient term
into an alongsigma component and a hydrostatic correction (for details, see Haidvogel and Beckmann, 1999).
In the horizontal, the primitive equations are evaluated using boundaryfitted, orthogonal curvilinear coordinates
on a staggered Arakawa Cgrid. The general formulation of curvilinear coordinates includes both Cartesian
(constant metrics) and spherical (variable metrics) coordinates.
Coastal boundaries can also be specified as a finitediscretized grid via land/sea masking.
As in the vertical, the horizontal stencil utilizes a centered, secondorder finite differences.
However, the code is designed to make the implementation of higher order stencils easily.
ROMS has various options for advection schemes: second and forthorder centered differences;
and thirdorder, upstream biased. The later scheme is the model default and it has a velocitydependent
hyperdiffusion dissipation as the dominant truncation error (Shchepetkin and McWilliams, 2005).
These schemes are stable for the predictorcorrector methodology of the model.
In addition, there is an option for conservative parabolic spline representation of vertical advection
which has dispersion properties similar to an eightorder accurate conventional scheme.
There are several subgridscale parameterizations in ROMS. The horizontal mixing of momentum and tracers can
be along vertical levels, geopotential (constant depth) surfaces, or isopycnic (constant density) surfaces.
The mixing operator can be harmonic (3point stencil) or biharmonic (5point stencil).
See Haidvogel and Beckmann (1999) for an overview of all these operators.
The vertical mixing parameterization in ROMS can be either by local or nonlocal closure schemes.
The local closure schemes are based on the level 2.5 turbulent kinetic energy equations by Mellor and Yamada (1982)
and the Generic Length Scale (GLS) parameterization (Umlauf and Burchard, 2003).
The nonlocal closure scheme is based on the Kprofile, boundary layer formulation by Large et al. (1994).
The Kprofile scheme has been expanded to include both surface and bottom oceanic boundary layers.
The GLS is a twoequation turbulence model that allows a wide range of vertical mixing closures,
including the popular kkl (MellorYamada level 2.5), ke, and kw schemes.
Currently, the airsea interaction boundary layer in ROMS is based on the bulk parameterization of Fairall et al. (1996).
It was adapted from the COARE (Coupled OceanAtmosphere Response Experiment) algorithm for the computation
of surface fluxes of momentum, sensible heat, and latent heat.
This boundary layer is used for one or twoway coupling with atmospheric models.
ROMS is a very modern code and uses Cpreprocessing to activate the various physical and numerical options.
The code can be run in either serial or parallel computers.
The code uses a coarsegrained parallelization paradigm which partitions the computational 3D grid into tiles.
Each tile is then operated on by different parallel threads.
Originally, the code was designed for sharedmemory computer architectures and the parallel compilerdependent
directives (OpenMP Standard) are placed only in the main computational routine of the code.
An MPI version of the code has been developed so both shared and distributedmemory paradigms coexist together in a single code.
ROMS is a very modern and modular code written in F90/F95.
It uses Cpreprocessing to activate the various physical and numerical options.
Several coding standards have been established to facilitate model readability, maintenance, and portability.
All the state model variables are dynamically allocated and passed as arguments to the computational routines
via dereferenced pointer structures. All private or scratch arrays are automatic;
their size is determined when the procedure is entered. This code structure facilitates computations
over nested and composed grids. The parallel framework is coarsegrained with both shared
and distributedmemory paradigms coexisting in the same code. The sharedmemory option follows OpenMP 2.0 standard.
ROMS has a generic distributedmemory interface that facilitates the use of several message passage protocols.
Currently, the data exchange between nodes is done with MPI.
However, other protocols like MPI2, SHMEM, and others can be coded without much effort.
ROMS has extensive pre and postprocessing software for data preparation, analysis, plotting, and visualization.
The entire input and output data structure of the model is via NetCDF which facilitates the interchange of data
between computers, user community, and other independent analysis software.
Model Grid and geometry
The model uses Cartesian grid with horizontal resolution of 10  30 m.
Model domain size: 400x400 grid points with 10 vertical levels.
Sigma (terrainfollowing) levels are uniformly distributed.
Topography is extracted from an interactively generated bathymetry file for the domain,
see the description of the interpolation method below. Land/sea masking for rho, u, v and psi grids
are calculated accordingly. Grid parameters: pm, pn, x_rho, y_rho, x_psi, y_psi, x_u, y_u, x_v, y_v
are extracted from analytical grid calculated by the model using ANA_GRID option.
Coriolis factor is set to constant f=0.0001 s1
Model options
for setup with open boundary conditions, analytical tides, analytical salinity input and mm5 surface forcing.
For the simulation of phosphogypsum, the sediment transport option of ROMS was used, simulating
the phosphogypsum sludge as a “cohesive sediment”, including the simulation of transport,
deposition and erosion. Suspended sediment results depend very much on bottom stress
and vertical mixing (see, for example: http://woodshole.er.usgs.gov/project pages/sedimenttransport/
Sediment parameters
For the simulation of the phosphogypsum sludge release, ROMS is used with the (cohesive) sediment options;
the set of sediment related parameters that need to be defined for the final scenario analysis are listed below.
The initial granulometry for the sediments is related to literature values (Fakhri et al., 2008), see below, updated with field measurements.
From:
Milad Fakhri, Marie Abboud  Abi Saab and JeanClaude Romano
(2008) : THE USE OF SEDIMENTS TO ASSESS THE IMPACT OF SELAATA PHOSPHATE PLANT ON BATROUN COASTAL AREA (LEBANON, LEVANTINE BASIN)
Lebanese Science Journal, Vol. 9, No. 1, 2008
