2.2 Shelf scale modelling: SURF
2.2.1 SURF model characteristics
In this section we describe the technical characteristics of the SURF standard structured grid component and the SURF model work-flow.
Governing equations, spatial discretization, surface, bottom and lateral closed boundary conditions are described in details in section2.1.1, since SURF struc-tured component is based on NEMO-OPA code (version 3.6).
In the following we mainly refer to Trotta et al.(2016).
2.2.1.1 Horizontal and vertical grids
The horizontal grid is a regularly spaced latitude/longitude grid in a spherical coordinate system: it has coordinate axes aligned with parallels and meridians and constant spacing in both latitude and longitude directions. Hence, it is simply defined by setting the number of points and the grid sizes in the zonal
40 Chapter 2. Large scale and shelf scale numerical models
and meridional directions, and the reference longitude and latitude coordinate of the lower left corner of the T-grid.
In the vertical direction, SURF employs N = 100 stretched z-coordinate vertical layers which are distributed in such a way as to better resolve the surface and intermediate layers: the nearly uniform vertical locations of levels at the ocean top and bottom, with distances between consecutive layers shorter at the top (minimum distance: 0.6 m) than at the bottom (maximum: 18 m), are divided by a smooth hyperbolic tangent transition.
Thus, according to what prescribed in the NEMO code (Madec and the NEMO team,2016), the locations of the T-grid vertical levels are given by the following analytic expression:
where k indicates the vertical level considered (k = 1, 2, ..., N ), hcr denotes the stretching factor of the grid, hth the approximate model level at which maxi-mum stretching occurs and hsur, h0, h1 are defined from hcr, hth, the number of vertical levels N , the maximum depth zmax and the top layer minimum thickness dzmin.
Partial cell parametrisation is used: the first vertical level located under z =
−H is shifted to z = −H, so that the bottom layer thickness varies with geographical location, following the real bathymetry.
2.2.1.2 Time-steps
To solve the three-dimensional prognostic equations for active tracers and mo-mentum, SURF adopts the split-explicit free surface (or time-splitting) formu-lation (Griffies,2004), separating the fast barotropic part (e.g. fast propagating external gravity waves) and the slow baroclinic part of the dynamics.
Baroclinic velocities and tracers, depth dependant prognostic variables that evolve more slowly, are solved with a larger time-step ∆t (depending on the horizontal resolution, in order to satisfy the CFL condition); the barotropic part of the dynamical equations (the free surface equation and the associated barotropic velocity equations), instead, is integrated explicitly with a shorter time-step ∆te (the external mode or barotropic time-step), which is provided through the name-list parameter nn_baro as: ∆te = ∆t/nn_baro. nn_baro must also be chosen in such a way as to make ∆te satisfy the CFL criterion.
2.2. Shelf scale modelling: SURF 41
2.2.1.3 Open boundary conditions
Because of the adoption of the time-splitting formulation (see paragraph2.2.1.2), the lateral open boundary conditions must be formulated separately for the barotropic and baroclinic modes. The algorithms used are the Flather scheme for barotropic velocities and sea surface height and the Flow relaxation scheme for baroclinic velocities and active tracers.
Given the particular importance that open boundary conditions hold in the dynamical downscaling problem, they are treated separately in section2.2.2.
2.2.1.4 Diffusivity and viscosity coefficients
The horizontal eddy diffusivity and viscosity coefficients, constant in space and time, can be directly specified through the correspondent name-list parameters or they can be obtained from the parent coarse resolution model ones. In the latter case, if a0 is e.g. the parent viscosity, the child correspondent coefficient is a = a0∆x∆xF
L
m
, where ∆xF and ∆xLare respectively the fine and large scale model grid spacings and m is to be chosen on the basis of the model numerical stability issues and on the basis of the parametrisations used for sub-grid scale lateral mixing (see section2.1.1.1).
The vertical eddy viscosity and diffusivity coefficients are computed following the Richardson-number dependent scheme ofPacanowski and Philander(1981).
Where there might be unstable stratification, they are replaced by a higher value of 10 ms2.
2.2.1.5 SURF work-flow
SURF works on a Linux virtual machine environment where the three model components (written in fortran), inputs data, numerical outputs and several pre- and post-processing tools (written in NCL, NCO and python and specifi-cally developed for SURF) are reciprospecifi-cally connected.
The user has to initially choose the simulation parameters for NEMO. When these are set, the system accesses the following input datasets: bathymetry, coastline, parent model u, v, T , S and η fields and atmospheric forcings.
After these first two steps, the numerical grid is generated and data are refor-matted, computing the atmospheric forcing, bathymetry, boundary and initial conditions datasets on the child grid through interpolation. This is done using the sea-over-land procedure (Kara,2007;De Dominicis,2014): this method is necessary to provide the input fields in the areas near the coast where the parent model variables are not defined, due to the coarser representation of bathymetry
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and coastline on the large-scale model grid. The sea-over-land procedure hor-izontally extrapolates the coarse resolution model ocean variables on the land grid points for each vertical level, in order to interpolate these quantities to the child grid in between. This is applied also to atmospheric fields, so as to avoid land contaminations near the coast, given the different characteristics of sea and land boundary layers. To perform the interpolation a bilinear method is used in the horizontal (only for the structured grid component), while a linear one is adopted in the vertical direction.
As a final step, numerical integration produces the outputs, which can be displayed in the SURF virtual machine thanks to the post-processing tools present.
Figure 2.2: SURF work-flow. Reproduced fromTrotta et al.(2016).
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