Résumé The ocean engine of NEMO (Nucleus for European Modelling of the Ocean) is a primitive equation model adapted to regional and global ocean circulation problems. It is intended to be a flexible tool for studying the ocean and its interactions with the others components of the earth climate system over a wide range of space and time scales. Prognostic variables are the three-dimensional velocity field, a linear or non-linear sea surface height, the temperature and the salinity. In the horizontal direction, the model uses a curvilinear orthogonal grid and in the vertical direction, a full or partial step z-coordinate, or s-coordinate, or a mixture of the two. The distribution of variables is a three-dimensional Arakawa C-type grid. Various physical choices are available to describe ocean physics, including TKE, GLS and KPP vertical physics. Within NEMO, the ocean is interfaced with a sea-ice model (LIM v2 and v3), passive tracer and biogeochemical models (TOP) and, via the OASIS coupler, with several atmospheric general circulation models. It also support two-way grid embedding via the AGRIF software. Le moteur océanique de NEMO (Nucleus for European Modelling of the Ocean) est un modèle aux équations primitives de la circulation océanique régionale et globale. Il se veut un outil flexible pour étudier sur un vaste spectre spatiotemporel l’océan et ses interactions avec les autres composantes du système climatique terrestre. Les variables pronostiques sont le champ tridimensionnel de vitesse, une hauteur de la mer linéaire ou non, la temperature et la salinité. La distribution des variables se fait sur une grille C d’Arakawa tridimensionnelle utilisant une coordonnée verticale z à niveaux entiers ou partiels, ou une coordonnée s, ou encore une combinaison des deux. Différents choix sont proposés pour décrire la physique océanique, incluant notamment des physiques verticales TKE, GLS et KPP. A travers l’infrastructure NEMO, l’océan est interfacé avec des modèles de glace de mer, de biogéochimie et de traceurs passifs, et, via le coupleur OASIS, à plusieurs modèles de circulation générale atmosphérique. Il supporte également l’emboı̂tement interactif de maillages via le logiciel AGRIF.

NEMO ocean engine

[1] Discretization of the pressure-gradient force is a long-standing problem in terrain-following (or σ) coordinate oceanic modeling. When the isosurfaces of the vertical coordinate are not aligned with either geopotential surfaces or isopycnals, the horizontal pressure gradient consists of two large terms that tend to cancel; the associated pressure-gradient error stems from interference of the discretization errors of these terms. The situation is further complicated by the nonorthogonality of the coordinate system and by the common practice of using highly nonuniform stretching for the vertical grids, which, unless special precautions are taken, causes both a loss of discretization accuracy overall and an increase in interference of the component errors. In the present study, we design a pressure-gradient algorithm that achieves more accurate hydrostatic balance between the two components and does not lose as much accuracy with nonuniform vertical grids at relatively coarse resolution. This algorithm is based on the reconstruction of the density field and the physical z coordinate as continuous functions of transformed coordinates with subsequent analytical integration to compute the pressure-gradient force. This approach allows not only a formally higher order of accuracy, but it also retains and expands several important symmetries of the original second-order scheme to high orders [Mellor et al., 1994; Song, 1998], which is used as a prototype. It also has built-in monotonicity constraining algorithm that prevents appearance of spurious oscillations of polynomial interpolant and, consequently, insures numerical stability and robustness of the model under the conditions of nonsmooth density field and coarse grid resolution. We further incorporate an alternative method of dealing with compressibility of seawater, which escapes pressure-gradient errors associated with interference of the nonlinear nature of equation of state and difficulties to achieve accurate polynomial fits of resultant in situ density profiles. In doing so, we generalized the monotonicity constraint to guarantee nonnegative physical stratification of the reconstructed density profile in the case of compressible equation of state. To verify the new method, we perform traditional idealized (Seamount) and realistic test problems.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2001JC001047

A method for computing horizontal pressure-gradient force in an oceanic model with a nonaligned vertical coordinate

This paper addresses the structure and dynamical mechanisms of regional and mesoscale physical variability in the subtropical northeast Pacific Ocean using the Regional Oceanic Modeling System (ROMS). The model is configured with a U.S. West Coast domain that spans the California Current System (CCS) with a mesoscale horizontal resolution up to as fine as 3.5 km. Its mean-seasonal forcing is by momentum, heat, and water fluxes at the surface and adaptive nudging to gyre-scale fields at the open water boundaries. Its equilibrium solutions show realistic mean and seasonal states and vigorous mesoscale eddies, fronts, and filaments. The level of eddy kinetic energy (EKE) in the model is comparable to drifter and altimeter estimates in the solutions with sufficiently fine resolution. Because the model lacks nonseasonal transient forcing, the authors conclude that the dominant mesoscale variability in the CCS is intrinsic rather than transiently forced. The primary eddy generation mechanism is the baroclinic instability of upwelling, alongshore currents. There is progressive movement of meanseasonal currents and eddy energy offshore and downward into the oceanic interior in an annually recurrent cycle. The associated offshore eddy heat fluxes provide the principal balance against nearshore cooling by mean Ekman transport and upwelling. The currents are highly nonuniform along the coast, with important influences by capes and ridges in both maintaining mean standing eddies and launching transient filaments and fronts.

https://journals.ametsoc.org/doi/pdf/10.1175/1520-0485%282003%2933%3C753%3AESADOT%3E2.0.CO%3B2

Equilibrium structure and dynamics of the California Current System

This book provides an introductory-level exploration of geophysical fluid dynamics (GFD), the principles governing air and water flows on large terrestrial scales. Physical principles are illustrated with the aid of the simplest existing models, and the computer methods are shown in juxtaposition with the equations to which they apply. It explores contemporary topics of climate dynamics and equatorial dynamics including the Greenhouse Effect, global warming, and the El Nino Southern Oscillation. It combines both physical and numerical aspects of geophysical fluid dynamics into a single affordable volume. It explores contemporary topics such as the Greenhouse Effect, global warming and the El Nino Southern Oscillation. Biographical and historical notes at the ends of chapters trace the intellectual development of the field. This title is written by recipient of the 2010 Wernaers Prize, awarded each year by the National Fund for Scientific Research of Belgium (FNR-FNRS).

Introduction to Geophysical Fluid Dynamics, Physical and Numerical Aspects, 2nd Edition Volume 101

Developments in ocean climate modelling

A Jacobian formulation of the pressure gradient force for use in models with topography-following coordinates is proposed. It can be used in conjunction with any vertical coordinate system and is easily implemented. Vertical variations in the pressure gradient are expressed in terms of a vertical integral of the Jacobian of density and depth with respect to the vertical computational coordinate. Finite difference approximations are made on the density field, consistent with piecewise linear and continuous fields, and accurate pressure gradients are obtained by vertically integrating the discrete Jacobian from sea surface. Two discrete schemes are derived and examined in detail: the first using standard centered differencing in the generalized vertical coordinate and the second using a vertical weighting such that the finite differences are centered with respect to the Cartesian z coordinate. Both schemes achieve second-order accuracy for any vertical coordinate system and are significantly more a...

Y. Tony Song

Papers

A General Pressure Gradient Formulation for Ocean Models. Part I: Scheme Design and Diagnostic Analysis