% ================================================================ % INTRODUCTION % ================================================================ \chapter{Introduction} The Nucleus for European Modelling of the Ocean (\NEMO) is a framework of ocean related engines, namely OPA\footnote{OPA = Oc\'{e}an PArall\'{e}lis\'{e}} for the ocean dynamics and thermodynamics, LIM\footnote{LIM= Louvain)la-neuve Ice Model} for the sea-ice dynamics and thermodynamics, TOP\footnote{TOP = Tracer in the Ocean Paradigm} for the biogeochemistry (both transport (TRP) and sources minus sinks (LOBSTER, PISCES)\footnote{Both LOBSTER and PISCES are not acronyms just name}. It is intended to be a flexible tool for studying the ocean and its interactions with the other components of the earth climate system (atmosphere, sea-ice, biogeochemical tracers, ...) over a wide range of space and time scales. This documentation provides information about the physics represented by the ocean component of \NEMO and the rationale for the choice of numerical schemes and the model design. More specific information about running the model on different computers, or how to set up a configuration, are found on the \NEMO web site (www.locean-ipsl.upmc.fr/NEMO). The ocean component of \NEMO has been developed from the OPA model, release 8.2, described in \citet{Madec1998}. This model has been used for a wide range of applications, both regional or global, as a forced ocean model and as a model coupled with the atmosphere. A complete list of references is found on the \NEMO web site. This manual is organised in as follows. Chapter~\ref{PE} presents the model basics, $i.e.$ the equations and their assumptions, the vertical coordinates used, and the subgrid scale physics. This part deals with the continuous equations of the model (primitive equations, with potential temperature, salinity and an equation of state). The equations are written in a curvilinear coordinate system, with a choice of vertical coordinates ($z$ or $s$, with the rescaled height coordinate formulation \textit{z*}, or \textit{s*}). Momentum equations are formulated in the vector invariant form or in the flux form. Dimensional units in the meter, kilogram, second (MKS) international system are used throughout. The following chapters deal with the discrete equations. Chapter~\ref{DOM} presents the space and time domain. The model is discretised on a staggered grid (Arakawa C grid) with masking of land areas and uses a Leap-frog environment for time-stepping. Vertical discretisation used depends on both how the bottom topography is represented and whether the free surface is linear or not. Full step or partial step $z$-coordinate or $s$- (terrain-following) coordinate is used with linear free surface (level position are then fixed in time). In non-linear free surface, the corresponding rescaled height coordinate formulation (\textit{z*} or \textit{s*}) is used (the level position then vary in time as a function of the sea surface heigh). The following two chapters (\ref{TRA} and \ref{DYN}) describe the discretisation of the prognostic equations for the active tracers and the momentum. Explicit, split-explicit and implicit free surface formulations are implemented as well as rigid-lid case. A number of numerical schemes are available for momentum advection, for the computation of the pressure gradients, as well as for the advection of tracers (second or higher order advection schemes, including positive ones). Surface boundary conditions (chapter~\ref{SBC}) can be implemented as prescribed fluxes, or bulk formulations for the surface fluxes (wind stress, heat, freshwater). The model allows penetration of solar radiation There is an optional geothermal heating at the ocean bottom. Within the \NEMO system the ocean model is interactively coupled with a sea ice model (LIM) and with biogeochemistry models (PISCES, LOBSTER). Interactive coupling to Atmospheric models is possible via the OASIS coupler \citep{OASIS2006}. Other model characteristics are the lateral boundary conditions (chapter~\ref{LBC}). Global configurations of the model make use of the ORCA tripolar grid, with special north fold boundary condition. Free-slip or no-slip boundary conditions are allowed at land boundaries. Closed basin geometries as well as periodic domains and open boundary conditions are possible. Physical parameterisations are described in chapters~\ref{LDF} and \ref{ZDF}. The model includes an implicit treatment of vertical viscosity and diffusivity. The lateral Laplacian and biharmonic viscosity and diffusion can be rotated following a geopotential or neutral direction. There is an optional eddy induced velocity \citep{Gent1990} with a space and time variable coefficient \citet{Treguier1997}. The model has vertical harmonic viscosity and diffusion with a space and time variable coefficient, with options to compute the coefficients with \citet{Blanke1993}, \citet{Large1994}, or \citet{PacPhil1981} mixing schemes. Specific online diagnostics (not documented yet) are available in the model: output of all the tendencies of the momentum and tracers equations, output of tracers tendencies averaged over the time evolving mixed layer. The model is implemented in \textsc{Fortran 90}, with preprocessing (C-pre-processor). It runs under UNIX. It is optimized for vector computers and parallelised by domain decomposition with MPI. All input and output is done in NetCDF (Network Common Data Format) with a optional direct access format for output. To ensure the clarity and readability of the code it is necessary to follow coding rules. The coding rules for OPA include conventions for naming variables, with different starting letters for different types of variables (real, integer, parameter\ldots). Those rules are presented in a document available on the \NEMO web site. The model is organized with a high internal modularity based on physics. For example, each trend ($i.e.$, a term in the RHS of the prognostic equation) for momentum and tracers is computed in a dedicated module. To make it easier for the user to find his way around the code, the module names follow a three-letter rule. For example, \mdl{tradmp} is a module related to the TRAcers equation, computing the DaMPing. The complete list of module names is presented in \colorbox{yellow}{annex}. Furthermore, modules are organized in a few directories that correspond to their category, as indicated by the first three letters of their name. The manual mirrors the organization of the model. After the presentation of the continuous equations (Chapter \ref{PE}), the following chapters refer to specific terms of the equations each associated with a group of modules . \begin{table}[htbp] \label{tab1} %\begin{center} \begin{tabular}{|p{143pt}|l|l|} \hline \begin{center} \begin{tabular}{|l|l|l|} \hline Chapter \ref{DOM} & DOM & model DOMain \\ \hline Chapter \ref{TRA} & TRA & TRAcer equations (potential temperature and salinity) \\ \hline Chapter \ref{DYN} & DYN & DYNamic equations (momentum) \\ \hline Chapter \ref{SBC} & SBC & Surface Boundary Conditions \\ \hline Chapter \ref{LBC} & LBC & Lateral Boundary Conditions \\ \hline Chapter \ref{LDF} & LDF & Lateral DiFfusion (parameterisations) \\ \hline Chapter \ref{ZDF} & ZDF & Vertical DiFfusion \\ \hline Chapter \ref{MISC} & ... & Miscellaneous topics \\ \hline \end{tabular} \end{center} \end{table} In the current release (v2.3), LBC directory (see Chap.~\ref{LBC}) does not yet exist. When created LBC will contain the OBC directory (Open Boundary Condition), and the \mdl{lbclnk}, \mdl{mppini} and \mdl{lib\_mpp} modules. \vspace{1cm} Nota Bene : \vspace{0.25cm} OPA, like all research tools, is in perpetual evolution. The present document describes the OPA version include in the release 3.0 of NEMO. This release differs significantly from version 8, documented in \citet{Madec1998}. The main modifications are :\\ (1) transition to full native \textsc{Fortran} 90, deep code restructuring and drastic reduction of CPP keys; \\ (2) introduction of partial step representation of bottom topography \citep{Barnier_al_OD06}; \\ (3) partial reactivation of a terrain-following vertical coordinate ($s$- and hybrid $s$-$z$) with the addition of several options for pressure gradient computation \footnote{Partial support of $s$-coordinate: there is presently no support for neutral physics in $s$- coordinate and for the new options for horizontal pressure gradient computation with a non-linear equation of state.}; \\ (4) more choices for the treatment of the free surface: full explicit, split-explicit , filtered and rigid-lid; \\ (5) non linear free surface option (associated with the rescaled height coordinate \textit{z*} or \textit{s*}); \\ (6) additional schemes for vector and flux forms of the momentum advection; \\ (7) additional advection schemes for tracers; \\ (8) implementation of the AGRIF package (Adaptative Grid Refinement in \textsc{Fortran}) \citep{Debreu_al_CG2008}; \\ (9) online diagnostics : tracers trend in the mixed layer and vorticity balance; \\ (10) rewriting of the I/O management; \\ (11) OASIS 3 and 4 couplers interfacing with atmospheric global circulation models. (12) surface module (SBC) that simplify the way the ocean is forced and include two bulk formulea (CLIO and CORE) (13) introduction of LIM 3, the new Louvain-la-Neuve sea-ice model (C-grid rheology and new thermodynamics including bulk ice salinity) In addition, several minor modifications in the coding have been introduced with the constant concern of improving performance on both scalar and vector computers.